Question

A farmer grows 105 pounds of apples. He sells them to a grocer who divides them into 2 pound and 3 pound bags. If the grocer uses ten more of one sized bags than the other, how many bags of each did he use?

i think there are two answers but I want to make sure

Answer 1

Let x be a number of 2 pound bags and y be a number of 3 pound bags.
Case 1: If farmer used 10 more 2 pound bags, then x-y=10 and 2x+3y=150. From the first equation x=10+y and from the second 2(10+y)+3y=150 we obtain that 5y+20=150, then 5y=130 and y=26. Thus, x=36.
Case 2: If farmer used 10 more 3 pound bags, then y-x=10 and 2x+3y=150. From the first equation y=x+10 and 2x+3(x+10)=150. So, we have 5x+30=150 and 5x=120, x=24 and y=34.

There are two possible answers: 1. 36 two pound bags and 26 three pound bags; 2: 24 two pound bags and 34 three pound bags.