# Lynne bought a bag of grapefruit, 1frac{5}{8} pounds of apples, and 2frac{3}{16} pounds of bananas. The total weight of her purchases was 7frac{1}{2} pounds. How much did the bag of grapefruit weigh?

Lynne bought a bag of grapefruit, $1\frac{5}{8}$ pounds of apples, and $2\frac{3}{16}$ pounds of bananas. The total weight of her purchases was $7\frac{1}{2}$ pounds. How much did the bag of grapefruit weigh?
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Let us assume that the weight of the bag of grapefruit be x pounds

Given:

The weight of the bag of apples is:

The weight of the bag of bananas is:

The total weight of all of the bags that was purchased by Lynne is:

So, we can write:

$x+\frac{13}{8}+\frac{35}{16}=\frac{15}{2}\phantom{\rule{0ex}{0ex}}⇒x+\frac{26+35}{16}=\frac{15}{2}\phantom{\rule{0ex}{0ex}}⇒x+\frac{61}{16}=\frac{15}{2}\phantom{\rule{0ex}{0ex}}⇒x=\frac{15}{2}-\frac{61}{16}\phantom{\rule{0ex}{0ex}}⇒x=\frac{120-61}{16}\phantom{\rule{0ex}{0ex}}⇒x=\frac{59}{16}\phantom{\rule{0ex}{0ex}}⇒x=3\frac{11}{16}$

Hence, the weight of the bag of grapefruit is