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24 August, 07:22

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

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  1. 24 August, 08:52
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    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.
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