Question 1103449: 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 farmer Bill sold?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
You can work this kind of problem either "forwards" or "backwards". I have seen many students who have a preference for one method or the other... so let's look at both methods.
1. Working forwards...
He starts with x pounds of potatoes.
He sells 1/4 of them, leaving him with (3/4)x pounds.
He then sells 4/9 of what he has left; that means he still has 5/9. The number of pounds he has left is 5/9 of (3/4)x, or (5/12)x.
When he sells "4/5 of what he has left, plus the last 10 pounds", it means his last sale was 50 pounds.
So  --> 
He started with 120 pounds of potatoes.
CHECK:
start: 120 lb
first sale: 1/4 of 120 = 30; he has 120-30 = 90 lb left
second sale: 4/9 of 90 = 40; he has 90-40 = 50 lb left
last sale: 4/5 of 50, plus 10 more = 40+10 = 50; he has none left
2. Working backwards...
Again, the last sale being "4/5 of what he has left, plus the last 10 pounds" means his last sale was 50 pounds.
Before that, on his second sale, he sold 4/9 of what he had at the time, leaving him with 5/9 of what he had before the sale. So 5/9 of what he had before the sale is 50 pounds, which means before the second sale he had 90 pounds.
His first sale was 1/4 of what he started with, leaving him with 3/4 of what he started with. So 90 pounds is 3/4 of what he started with; that means he started with 120 pounds.
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