A shop owner spent $540 to purchase a stock of computer keyboards. If the price of each keyboard had been reduced by $2, he could have bought 3 more keyboards. Find the price of one keyboard.​

Answers

Answer 1

Answer:

Price before discount = $20 per keyboard

Price after discount = $18 per keyboard

Before the discount, you can buy 27 keyboards. After the discount, you can buy 30 keyboards.

===============================================

Work Shown:

k = cost of one keyboard before the price reduction

540/k = amount of keyboards purchased before the price reduction

k-2 = cost of one keyboard after the price reduction

540/(k-2) =  amount of keyboards purchased after the price reduction

540/(k-2) = (540/k) + 3

--------------

If you multiply both sides by the LCM k(k-2), then you'll clear out the fractions and we can solve for k like so

540/(k-2) = (540/k) + 3

540k = 540(k-2) + 3k(k-2)

540k = 540k - 1080 + 3k^2 - 6k

0 = 540k - 1080 + 3k^2 - 6k - 540k

0 = 3k^2 - 6k - 1080

3k^2 - 6k - 1080 = 0

3(k^2 - 2k - 360) = 0

k^2 - 2k - 360 = 0

(k - 20)(k + 18) = 0

k-20 = 0 or k+18 = 0

k = 20 or k = -18

We ignore the negative result because a negative price doesn't make sense.

--------------

If k = 20, then

540/k = 540/20 = 27

Meaning that you can buy 27 keyboards before the price reduction

In other words, (27 keyboards)*(20 dollars per keyboard) = 540 dollars total.

After the price reduction, the cost per keyboard is now k-2 = 20-2 = 18

We can now buy 540/(k-2) = 540/18 = 30 keyboards, which is an increase of 30-27 = 3 extra keyboards. This helps confirm we have the correct answer.  

Answer 2

Answer:

$20

Step-by-step explanation:

X: the price of a keyboard

Y: number of keyboards to buy (original)

The shop owner spent $540 to purchase a stock of computer keyboards, so:

XY=540

⇒X=540/Y

If the price of each keyboard had been reduced by $2, he could have bought 3 more keyboards:

(X-2)(Y+3)=540  

⇒3X-2Y=6

⇒3.540/Y – 2Y=6

⇒Y=27

⇒X=20

⇒ the price of one keyboard: $20


Related Questions

Nick spends 18% of his monthly budget on his rent payment, which is $700.

Which proportion can be used to calculate Nick’s total monthly budget?

Answers

Answer: [tex]\frac{700}{y} =\frac{18}{100}[/tex]

Step-by-step explanation: 18% is a fraction [tex]\frac{18}{100}[/tex]

In this case since 700 18% of the budget we can do the same thing with the budget being valued as y.[tex]\frac{700}{y}[/tex]

sqrt x^ 2 +7 -2*=x-1​

Answers

Answer:

No solution for X€®Step-by-step explanation:

HOPE IT HELPS OR NOT SURE !!!!!!

*SHOW STEPS PLEASE* You can verify the zeros of the function y=x^2+6x-7 by using a graph and finding where the graph ________

a) is at a maximum.
b) is at a minimum.
c) crosses the y-axis.
d) crosses the x-axis

Answers

The graph crosses the x axis, because your roots are the x axis, so if you find where it intercepts the graphs at your x axis those are your solution or “zeros”

V = I ( R + r )
r = ?

Answers

Answer:

r = [tex]\frac{V-IR}{I}[/tex]

Step-by-step explanation:

Given

V = I (R + r) ← distribute parenthesis

V = IR + Ir ( subtract IR from both sides )

V - IR = Ir ( divide both sides by I )

[tex]\frac{V-IR}{I}[/tex] = r

Please help me as fast as you can

Answers

Answer:

0.99

Step-by-step explanation:

divide 6.93 by 7.

Answer:

= 0.99

Step-by-step explanation:

We have the equation:

6.93 ÷ 7 = ?  

 [tex]\left[\begin{array}{ccccccc}&&0.&9&9\\7&&6.&9&3\\&&-&6&3\\\left&&&&6&3\\&&&-&6&3\\&&&&&0\end{array}\right][/tex]

       0 . 9   9        ↑    7    6 9  3      −6 3  ↓         6  3       −6  3       0

**PLEASE HELP**

Given: f(x) = 3x - 5, and g(x) = x² - 4x, find g(f(3))​

Answers

Answer and Step-by-step explanation:

Plug 3 in for f(x), then plug the result of f(x) into g(x).

f(3) = 3(3) - 5

f(3) = 9 - 5

f(3) = 4

g(4) = [tex](4)^2 - 4(4)[/tex]

g(4) = 16 - 16

g(4) = 0

So, g(f(3)) = 0

#teamtrees #PAW (Plant And Water)

Answer:

0 is the final answer

Step-by-step explanation:

Substitute given values for x accordingly

Please please help me with this

Answers

I think it is K, M, and L

Step-by-step explanation:

i think is k , m , l

bcause 4 is the smallest number,

and 12 is the biggest number.

Need help with this geometry question

Answers

Answer:

I think it's 6 (square root) 2

Traci spent hour eating breakfast and
į hour helping clean up after breakfast.
How much time did she spend in all?
Give your answer in simplest form.
hour
Enter
Plz help

Answers

in order to add the two fractions together, you need to get them to the same denominator so
1/3=2/6
2/6+1/6= 3/6
But 3/6 is not in it’s simplest form so 3 and 6 are both divisible by 3 so it would be 1/2. the answer is 1/2

¿Qué tiempo será necesario para que $ 2.340.260 se conviertan en $3.393.377 al 1,25% de interés simple mensual?

Answers

Answer:

The right solution is "36 years".

Step-by-step explanation:

Given:

Principle,

P = $2,340,260

Amount,

A = $3,393,377

Simple interest,

SI = 3,393,377 - 2,340,260

   = $1,053,117

Rate of interest,

r = 1.25%

As we know,

⇒ [tex]SI=\frac{Prt}{100}[/tex]

By substituting the values, we get

⇒ [tex]1053117=\frac{2340260\times 1.25\times t}{100}[/tex]

⇒ [tex]10531170=292532.5\times t[/tex]

⇒              [tex]t=\frac{10531170}{292532.5}[/tex]

⇒                [tex]=36 \ years[/tex]

can anyone help with these four⁉️ Will mark brainliest:D !!

Answers

Answer:

Step-by-step explanation:

how can the position of a certain value in a given set of data be described and used in solving real-life problems?

Answers

Statisticians often talk about the position of a value, relative to other values in a set of data. The most common measures of position are percentiles, quartiles, and standard scores (aka, z-scores).

Percentiles
Assume that the elements in a data set are rank ordered from the smallest to the largest. The values that divide a rank-ordered set of elements into 100 equal parts are called percentiles.

An element having a percentile rank of Pi would have a greater value than i percent of all the elements in the set. Thus, the observation at the 50th percentile would be denoted P50, and it would be greater than 50 percent of the observations in the set. An observation at the 50th percentile would correspond to the median value in the set.

Quartiles
Quartiles divide a rank-ordered data set into four equal parts. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively. The chart below shows a set of four numbers divided into quartiles.

Eight numbers: 1, 2, 3, 4, 5, 6, 7, 8
Note the relationship between quartiles and percentiles. Q1 corresponds to P25, Q2 corresponds to P50, and Q3 corresponds to P75. Q2 is the median value in the set.

While measures of central tendency, dispersion, and skewness are used often in statistics, there are other methods of characterizing or describing data distributions or portions that are commonly used as well. We will examine several of these statistical measures, some of which you may already know or have seen elsewhere.


Standard Scores (z-Scores)
A standard score (aka, a z-score) indicates how many standard deviations an element is from the mean. A standard score can be calculated from the following formula.

z = (X - μ) / σ

where z is the z-score, X is the value of the element, μ is the mean of the population, and σ is the standard deviation.

Here is how to interpret z-scores.

A z-score less than 0 represents an element less than the mean.
A z-score greater than 0 represents an element greater than the mean.
A z-score equal to 0 represents an element equal to the mean.
A z-score equal to 1 represents an element that is 1 standard deviation greater than the mean; a z-score equal to 2, 2 standard deviations greater than the mean; etc.
A z-score equal to -1 represents an element that is 1 standard deviation less than the mean; a z-score equal to -2, 2 standard deviations less than the mean; etc.

The distance between points A and B is?

Answers

Answer:

√85

Step-by-step explanation:

A (-3 , 4)    B (4 , -2)

AB² = (4 - -3)² + (-2 -4)² = 49 + 36 = 85

AB = √85

What is the value of x?

Answers

Answer:

i dont know but the answer will be 1

-4х + 5y=— 28
4x – 3y = 20

Answers

I hope it's correct and it helps I don't know how to explain it lol

Please helpbajshsjs please anyways thanks a lot

Answers

Answer:

225 cm cubed

Step-by-step explanation:

(1/2•base)•height

Three boys and four girls enter a contest at the local movie theater. A randomly chosen winner will be awarded a free movie ticket, a collectible poster, or free popcorn. What is the probability that a girl will win free popcorn?

A. 3/21

B. 4/21

C. 3/7

D. 4/7

Answers

Answer:

D. 4/7

Step-by-step explanation:

There are 7 people in people and there are 4 girls, that would be 4/7.

pls answer this for me now

Answers

Answer:

(3) 48

Step-by-step explanation:

The angle inside the ABC one is two times its angle size

For every 5 balloons in the sky, 2 of them will be rainbow. If there was 150 of them in the sky, how many would be rainbow?

Answers

60 -> 2 times 150 then you divide it by 5.
Set up the proportion: 2/5=x/150
Cross multiply: 5x=300
Answer= 60 rainbow balloons

Ann borrowed $800 for 4 years the yearly interest was 16% how much interest did she owe after 4 years

Answers

Answer:

$512

Step-by-step explanation:

Interest = 16% of 800

             = 16/100 x 800

             = $128

Interest for 4 years = 128 x 4

                                = $512

which equation has x=4 as the solution

Answers

(1) step by step below

Comes with a picture
multiple-choice answer please help I need immediate help
Thank youuuu

Answers

Answer:

The answer is A. 31,250.

Step-by-step explanation:

To solve for the 7th term in the geometric sequence, start by plugging 7 into the explicit formula, and the formula will look like [tex]a_{7}=2*5^{(7-1)}[/tex].

Next, subtract 1 from 7, and the formula will look like [tex]a_{7}=2*5^{6}[/tex].

Then, raise 5 to the power of 6, which will look like [tex]2*15625[/tex].

Finally, multiply 2 by 15,625, and the answer will be 31,250.

Ophelia spins each of the three shown spinners once. What is the probability that the first spinner will land on A, the second on 4, and the third on Green? Enter your answer as a fraction in simplest form. Use / to write your fraction.

Answers

Answer:

1 /24

Step-by-step explanation:

Given the 3 spinners :

Probability = required outcome / Total possible outcomes

Probability that Spinner 1 lands on A :

P(spinner 1 lands on A) = 1/2

Probability that spinner 2 lands on 4 :

P(lands on 4) = 1 / 4

Probability that spinner 3 lands on green :

P(lands on green) = 1/3

Combined probability = 1/2 * 1/4 * 1/3 = 1 /24

A calculator which is marked at $120 is sold for cash at a 30% discount. How much change would Susan receive if she pays for the calculator with a $100 bill?

Answers

Answer:

64 dollars

Step-by-step explanation: 120×30%= $36-$100= $64

She receives $16 when she pays for the calculator with a $100 bill

What is the percentage?

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A calculator which is marked at $120 is sold for cash at a 30% discount.

So, It was sold for 70% of its mark value assuming that to x.

(70/100)×120 = x.

x = $84.

So, Susan will receive $(100 - 84) = $16.

learn more about percentages here :

https://brainly.com/question/24159063

#SPJ2

Help me plsss!! Thanks

Answers

Answer: B or D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The answer must have 5! since it is a combinaiton of letters without any repeats. Since you want two words, its 2/5!

can someone pls help for brainlest

Answers

Answer:

6 x 8 = 48 yd2 (square yards)

Step-by-step explanation:

Answer:

Area of triangle is 23 yd².

Step-by-step explanation:

Given :-

Base of triangle = 8 yd

Height of triangle = 6 yd

To find

Area of triangle

Solution :-

we know that,

Area of triangle = 1 / 2 × base × height

substitute the values

Area of triangle = 1/2 × 8 yd × 6 yd

multiplying the values

Area of triangle = 1/2 × 46 yd²

divide the values

Area of triangle = 46 yd ² /2 = 23 yd².

Therefore, Area of triangle is 23 yd ².

does anyone know the answer?

Answers

Answer:

x = 145

Step-by-step explanation:

The angles are same side exterior angle and same side exterior angles are supplementary

x +35 =180

Subtract 35 from each side

x = 180-35

x =145

Answer:

x=145

Step-by-step explanation:

180 -35 = 145

angle in a straight line add up to 180

x=145

F angle /corresponding angle are the same

Jane and Tannic split the cost of buying a video game. The game costs$25, and the sales is 6% markup. How much do they each pay?

Answers

Given:

The cost of game = $25

Sales markup = 6%

To find:

How much do they each pay?

Solution:

The sales markup is 6% of the cost.

[tex]\text{Sales markup}=25\times \dfrac{6}{100}[/tex]

[tex]\text{Sales markup}=1.5[/tex]

Now, the total cost after sales markup is:

[tex]25+1.5=26.5[/tex]

Jane and Tannic split the cost of buying a video game. It means they divide the cost in two equal parts. So, the amount paid by each one is

[tex]\dfrac{26.5}{2}=13.25[/tex]

Therefore, Jane and Tannic will pay $13.25 each .

Complete the angle addition postulate for the following angle

Answers

Given:

A figure and an incomplete equation [tex]m\angle GEM+m\angle MEO+m\angle \_\_[/tex].

To find:

The missing value for the given equation by using the angle addition postulate.

Solution:

A ray EM divides the angle GEO into two parts. The first part is [tex]\angle GEM[/tex] and the second part is [tex]\angle MEO[/tex].

Using the angle addition postulate [tex]\angle GEO[/tex] is the sum of [tex]\angle GEM[/tex] and [tex]\angle MEO[/tex].

[tex]m\angle GEM+m\angle MEO+m\angle GEO[/tex]

Therefore, the missing value is GEO and the complete equation is [tex]m\angle GEM+m\angle MEO+m\angle GEO[/tex].

Someone please help me with this lol… have no idea what I’m doing

Answers

Given:

[tex]\cos \theta =\dfrac{3}{5}[/tex]

[tex]\sin \theta <0[/tex]

To find:

The quadrant of the terminal side of [tex]\theta[/tex] and find the value of [tex]\sin\theta[/tex].

Solution:

We know that,

In Quadrant I, all trigonometric ratios are positive.

In Quadrant II: Only sin and cosec are positive.

In Quadrant III: Only tan and cot are positive.

In Quadrant IV: Only cos and sec are positive.

It is given that,

[tex]\cos \theta =\dfrac{3}{5}[/tex]

[tex]\sin \theta <0[/tex]

Here cos is positive and sine is negative. So, [tex]\theta [/tex] must be lies in Quadrant IV.

We know that,

[tex]\sin^2\theta +\cos^2\theta =1[/tex]

[tex]\sin^2\theta=1-\cos^2\theta[/tex]

[tex]\sin \theta=\pm \sqrt{1-\cos^2\theta}[/tex]

It is only negative because [tex]\theta [/tex] lies in Quadrant IV. So,

[tex]\sin \theta=-\sqrt{1-\cos^2\theta}[/tex]

After substituting [tex]\cos \theta =\dfrac{3}{5}[/tex], we get

[tex]\sin \theta=-\sqrt{1-(\dfrac{3}{5})^2}[/tex]

[tex]\sin \theta=-\sqrt{1-\dfrac{9}{25}}[/tex]

[tex]\sin \theta=-\sqrt{\dfrac{25-9}{25}}[/tex]

[tex]\sin \theta=-\sqrt{\dfrac{16}{25}}[/tex]

[tex]\sin \theta=-\dfrac{4}{5}[/tex]

Therefore, the correct option is B.

Other Questions
An air-track glider attached to a spring oscillates between the 14.0 cm mark and the 71.0 cm mark on the track. The glider completes 12.0 oscillations in 34.0 s . You may want to review (Pages 391 - 393) . Part A What is the period of the oscillations I will give 25 points for it if solve this problem 1 pc8. Some chemicals, most often inorganic salts, in the laboratory have the nasty tendency to absorb water from theatmosphere. This property is called hygroscopicity. Anhydrous (water-free) Cupric Perchlorate [Cu(C104)2] weighs262.447g/mol, but after sitting on out on the benchtop absorbs water from the air and now weighs 370.540g/mol. Howmany water molecules did our Cupric Perchlorate absorb? How much money should be deposited in an account today that earns 4% compounded monthly so that it will accumulate to $10,000 in 5 years? The cost, c, of a ham sandwich at a deli varies directly with the number of sandwiches, n. If c = $54 when n is 9, what is the cost of the sandwiches when n is 3? Which question did he ask to divide the items in the two groups? What is the mass percentage of copper in a 250 g sample of brass. Brass is made of copper and zinc and copper content of the sample is 150 g Each year Capital Two retains 75 percent of its customers, and the annual discount rate is 5 percent. What annual retention rate doubles the value of a customer? HELP PLSSS I will give first person to answer this write BrainlyestI suck at math this is easy Read the myth King Midas and the Golden Touch.In ancient Greece, Midas, king of Phrygia, ruled a very wealthy land. One day, some farmhands brought a captured creature to King Midas. They wanted to know what to do with the creature. King Midas recognized the creature as Silenus, the tutor of Dionysus, god of merrymaking. King Midas ordered the farmhands to set Silenus free. For ten days and nights, King Midas took care of Silenus. Then, King Midas took Silenus back to Dionysus.Silenus and Dionysus were both very grateful to see one another again. Since King Midas was kind to Silenus, Dionysus offered to give Midas anything he wished. Unfortunately, King Midas made a foolish and greedy decision. He thought of the wealth that his land had and realized that he could have more. He asked Dionysus to give him the ability to touch anything and turn it into gold. Dionysus knew that this gift would bring trouble and heartache."Are you sure that is what you wish?" asked Dionysus skeptically."I am sure," affirmed King Midas.Dionysus waved his staff, which had a pinecone on top, and disappeared. King Midas was anxious to experiment with his new ability. On the way back to the palace, Midas touched a twig, and it turned into delicate, pure gold! Midas was ecstatic. He also turned a stone, an apple, and a door into gold. When the king reached the river, he washed his hands to see if his ability would disappear. Instead, the drops of water turned to delicate gold droplets.King Midas reached his home and immediately ordered a banquet. He feasted with his friends to celebrate the never-ending riches of his kingdom. Regrettably, the king discovered that his golden touch turned food and drink into solid gold. What could the king do? He needed to eat and drink in order to live. Just then, his beautiful daughter came dancing into the banquet hall, celebrating her father's good fortune. When she knelt down before her father, King Midas embraced her. The princess's beating heart stilled, and her warm body turned cold. King Midas shrank away in horror. His daughter was now a gold statue!King Midas wept golden tears of bitterness and regret. His own foolishness and greed had destroyed his daughter's life and his own. He begged to Dionysus for forgiveness and aid. Dionysus was merciful. He told King Midas to go the source of the Pactolus River and bathe in the water. The water would take away Midas's golden ability and return anything he had touched back to its original form. King Midas quickly set out for the Pactolus River and traveled to its source. He bathed in the river and filled a pitcher with its water. King Midas poured the water over the head of his daughter, and her heart began to beat again. Midas embraced his daughter, grateful that his most precious treasure was alive once again. Since that day, the Pactolus River has contained the gold of King Midas.Read the myth Cassandra's Wish.In the ancient city of Troy, there lived a beautiful princess, who was much beloved by Queen Hecuba and King Prima, the last king of Troy. Her name was Cassandra. She was virtuous, loved her city very much, and had a lot of respect for the Greek gods and goddesses.One day, Apollo, the god of prophecy, noticed Cassandra's extraordinary beauty. He approached the young maiden and offered her a deal. She could have anything she wished in exchange for a kiss. Cassandra was flattered by Apollo's attention and delighted at the possibility of a wish. She immediately agreed to the deal. Her wish was to be able to see the future. Since Apollo was the god of prophecy, he was able to make Cassandra a prophetess. Cassandra was thrilled!Suddenly, Cassandra had a horrible vision of Troy being destroyed. She was devastated and furious at the revelation that her beloved home would be ruined. What kind of gift had Apollo given her? Apollo demanded that Cassandra kiss him, for she had made a bargain with him. In her fury, Cassandra refused. Apollo was outraged and decided to punish this mortal. Cassandra would still be able to see the future, but no one would believe her predictions. From that day on, the citizens of Troy believed that Cassandra was slightly crazy and didn't believe her prophesies, even though they always came true. Cassandra lived a lonely life, waiting for her city to be destroyed and longing for the days before she had made her foolish wish.How do the authors use similar events in each passage to illustrate the theme that people should be careful with what they wish for?A. Both authors showed the main characters acting disrespectfully.B. Both authors showed the main characters regretting their requests.C. Both authors showed the main characters saving other people.D. Both authors showed the main characters using their abilities. There was a huge debate in the North about how to treat the South after winning the war. Lincoln and his successor Andrew Johnson, wanted to be lenient and forgiving on the South. The Radical Republicans wanted to punish the rebel leaders, take the land away from the plantation class and ensure equality for former slaves by using force with the army. Who do you think had the right approach to reconstruction and why? An elevator company has redesigned their product to be 50% more energy efficient than hydraulic designs. Two designs are being considered for implementation in a new building. (a) Given an interest rate of 20% which bid should be accepted? AlternativesInstalled costAnnual costSalvage valueLife, in years A$45,000 2700 3000 10 B$54,000 2850 4500 15(b) Research and list a few attributes that the company might be using in the elevators' major systems drive, cab, hoist, and control mechanisms that make them more energy efficient. What is the interquartile range of the data set shown below?25, 28, 32, 35, 36, 40, 46 How many grams of calcium chloride would you measure if you needed toadd 0.125 moles of calcium chloride to 100mL of water? How can diabetes insipidus be treated?a. Drugs that block ADH receptors can be administered to help increase urination and ensure liquid processing.b. Drugs such as corticosteroids can reduce unnecessary inflammation caused by damage to adrenal glands.c. Hormone reduction therapy can cause the body to reabsorb hormones that are produced in excess due to tumors.d. Hormone replacement therapy can replace ADH to help the kidneys retain water and stop excessive urination. If GH = HI And FI =10 what is GI Please help Ill give brainliest A density graph is used to find the probability of a discrete random variabletaking on a range of values.A. TrueB. False Sami wants to find the measures of the sides and angles of the parallelogram shown.Which tools can she use to find these measures? Protractor,Scale,compass .ruler select all that apply What is the meaning Media-saturatedPeer group Cachet Negotiating