Farmer Bill sold potatoes at the farm market. He sold a quarter to the first person, 4/9 of what was left to the second person, and the third buyer bought 4/5 of what was left and the last 10 lb. How many pounds of potatoes did farmer Bill sell?

Answer:

Farmer Bill sold 120 lb of potatoes

Step-by-step explanation:

Suppose farmer Bill had x lb of potatoes. He sold a quarter to the first person. A quarter is written as (1/4)x. After that, Bill had x-(1/4)x = (3/4)x.

Then he sold 4/9 of what was left to the second person, thus it was left 1-4/9=5/9 of the remaining potatoes. Multiplying both factors:

[tex]\frac{5}{9}*\frac{3}{4}x=\frac{5}{12}x[/tex]

This is the remaining portion of the potatoes.

Finally, he sold 4/5 of it and the last 10 lb. This means 1 - 4/5 = 1/5 of the remaining is equivalent to 10 lb:

[tex]\frac{1}{5}*\frac{5}{12}x=\frac{1}{12}x[/tex]

Thus:

[tex]\frac{1}{12}x=10[/tex]

x = 120 lb

Farmer Bill sold 120 lb of potatoes

The Farmer will sold 120 lb of potatoes.

Let us consider that farmer have x lb of potatoes.

He sold a quarter to the first person, that is  [tex]\frac{x}{4}[/tex]

Potatoes left,[tex]=x-\frac{x}{4} =\frac{3x}{4}[/tex]

4/9 of what was left to the second person,

 Potatoes sell to second person is, [tex]\frac{3x}{4} *\frac{4}{9} =\frac{x}{3}[/tex]

the third buyer bought 4/5 of what was left

       that is,          [tex]\frac{4}{5}*(\frac{3x}{4} -\frac{x}{3} ) =\frac{x}{3}[/tex]

Potatoes left [tex]=\frac{5x}{12} -\frac{x}{3} =\frac{x}{12}[/tex]

Since, Potatoes left = 10 lb

So,   [tex]\frac{x}{12} =10\\\\x=12*10=120[/tex]

Thus, The Farmer will sold 120 lb of potatoes.

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