Question 1103449
<br>
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.<br>
1. Working forwards...<br>
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 {{{(5/12)x = 50}}} --> {{{x = 120}}}<br>
He started with 120 pounds of potatoes.<br>
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<br>
2. Working backwards...<br>
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.