Question

Lynee bought some produce. She bought a bag of grapefruit, 1 5/8 pounds of apples, and 2 3/16 pounds of bananas. The total weight of her purchase was 7 1/2 pounds. How much did the bag of grapefruit weight?

Answer 1

Given:

Lynee bought a bag of grapefruit,
`1(5)/(8)` pounds of apples, and
`2(3)/(16)` pounds of bananas.

The total weight of her purchase was
`7(1)/(2)` pounds.

To find:

The weight of the bag of grapefruit.

Solution:

We have,

Weight of apples =
`1(5)/(8)` pounds.

Weight of bananas =
`2(3)/(16)` pounds.

Total weight of her purchase =
`7(1)/(2)` pounds.

Let x be the weight of the bag of grapefruit.

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

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

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

`(16x+26+35)/(16)=(15)/(2)`

Multiply both sides by 16.

`16x+61=120`

`16x=120-61`

`16x=59`

`x=(59)/(16)`

`x=3(11)/(16)`

Therefore, the weight of a bag of grapefruit is
`3(11)/(16)` pounds.