Question

Lynne bought a bag of grapefruit 1 3 pounds of apples and 2 pounds of bananas. The total weight of her purchases was 7 pounds. How much did the bag of grapefruit weigh

Answer 1

Let us call x the weight of the grapefruit bag. Then we know that the weight of the grapefruit bag plus 1 5 /8 pounds plus 2 3 /16 pounds must equal 7 1/2 pounds.

Therefore, we have

$x+1\frac{5}{8}+2\frac{3}{16}=7\frac{1}{2}$

The first step in simplifying the above is to convert each of the mixed numbers into improper fractions.

$1\frac{5}{8}=1+\frac{5}{8}=\frac{8}{8}+\frac{5}{8}=\frac{13}{8}$$2\frac{3}{16}=2+\frac{3}{16}=\frac{32}{16}+\frac{3}{16}=\frac{35}{16}$$7\frac{1}{2}=7+\frac{1}{2}=\frac{14}{2}+\frac{1}{2}=\frac{15}{2}$

hence, our equation becomes

$x+\frac{13}{8}+\frac{35}{16}=\frac{15}{2}$

Adding the fractions on the left gives (to do this we first find their common denominators and then add them up)

$x+\frac{61}{16}=\frac{15}{2}$

subtracting 61/16 from both sides gives

$x=\frac{15}{2}-\frac{61}{16}$

$x=\frac{59}{16}$

As a mixed number, this is

$x=3\frac{13}{16}$

Hence, the weight of the pag of grape