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(5)/(8)+2(3)/(16)=7(1)/(2)`

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

`1(5)/(8)=1+(5)/(8)=(8)/(8)+(5)/(8)=(13)/(8)`
`2(3)/(16)=2+(3)/(16)=(32)/(16)+(3)/(16)=(35)/(16)`
`7(1)/(2)=7+(1)/(2)=(14)/(2)+(1)/(2)=(15)/(2)`

hence, our equation becomes

`x+(13)/(8)+(35)/(16)=(15)/(2)`

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

`x+(61)/(16)=(15)/(2)`

subtracting 61/16 from both sides gives

`x=(15)/(2)-(61)/(16)`

`x=(59)/(16)`

As a mixed number, this is

`x=3(13)/(16)`

Hence, the weight of the pag of grape