Question

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

Answer 1

Weight of the bag of grapefruit =
`3(11)/(16)` pounds

Explanation:

Given :

Total weight of fruits purchased by Lynne =
`7(1)/(2)` pounds

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

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

To find the wight of the bag of grapefruit bought.

Solution:

Weight of the bag of grapefruit can be calculated by subtracting the weights of apples and bananas combined from the total weight.

Weight of apples and bananas combined =
`(1(5)/(8)+2(3)/(16))` pounds

Weight of the bag of grapefruit bought can be calculated as :

⇒
`7(1)/(2)-(1(5)/(8)+2(3)/(16))`

Simplifying by removing parenthesis by reversing the sign after the negative.

⇒
`7(1)/(2)-1(5)/(8)-2(3)/(16)`

Evaluating the whole numbers and fraction separately.

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

⇒
`(4)+((1)/(2)-(5)/(8)-(3)/(16))`

Taking LCD for 2,8,16 which is = 16 as its the least common multiple.

Making the denominators common.

⇒
`(4)+((1* 8)/(2* 8)-(5* 2)/(8* 2)-(3* 1)/(16* 1))`

⇒
`(4)+((8)/(16)-(10)/(16)-(3)/(16))`

Combining the numerators.

⇒
`(4)+((8-10-3)/(16))`

⇒
`(4)+((-5)/(16))`

Making whole number to fraction to evaluate.

⇒
`(4)/(1)-(5)/(16)`

Taking LCD = 16

⇒
`(4* 16)/(1* 16)-(5)/(16)`

⇒
`(64)/(16)-(5)/(16)`

Combining the numerators.

⇒
`(64-5)/(16)`

⇒
`(59)/(16)`

Converting to mixed number.

⇒
`3(11)/(16)` pounds (Answer)

Weight of the bag of grapefruit =
`3(11)/(16)` pounds