Question

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 1

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:

$\frac{5}{9}*\frac{3}{4}x=\frac{5}{12}x$

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:

$\frac{1}{5}*\frac{5}{12}x=\frac{1}{12}x$

Thus:

$\frac{1}{12}x=10$

x = 120 lb

Farmer Bill sold 120 lb of potatoes