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

Answer:

Weight of the bag of grapefruit = $3\frac{11}{16}$ pounds

Step-by-step explanation:

Given :

Total weight of fruits purchased by  Lynne = $7\frac{1}{2}$ pounds

Weight of apples purchased = $1\frac{5}{8}$ pounds

Weight of bananas =$2\frac{3}{16}$ 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 = $(1\frac{5}{8}+2\frac{3}{16})$ pounds

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

⇒ $7\frac{1}{2}-(1\frac{5}{8}+2\frac{3}{16})$

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

⇒ $7\frac{1}{2}-1\frac{5}{8}-2\frac{3}{16}$

Evaluating the whole numbers and fraction separately.

⇒ $(7-1-2)+(\frac{1}{2}-\frac{5}{8}-\frac{3}{16})$

⇒ $(4)+(\frac{1}{2}-\frac{5}{8}-\frac{3}{16})$

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

Making the denominators common.

⇒ $(4)+(\frac{1\times 8}{2\times 8}-\frac{5\times 2}{8\times 2}-\frac{3\times 1}{16\times 1})$

⇒ $(4)+(\frac{8}{16}-\frac{10}{16}-\frac{3}{16})$

Combining the numerators.

⇒ $(4)+(\frac{8-10-3}{16})$

⇒ $(4)+(\frac{-5}{16})$

Making whole number to fraction to evaluate.

⇒  $\frac{4}{1}-\frac{5}{16}$

Taking LCD = 16

⇒  $\frac{4\times 16}{1\times 16}-\frac{5}{16}$

⇒  $\frac{64}{16}-\frac{5}{16}$

Combining the numerators.

⇒  $\frac{64-5}{16}$

⇒  $\frac{59}{16}$

Converting to mixed number.

⇒  $3\frac{11}{16}$ pounds (Answer)

Weight of the bag of grapefruit = $3\frac{11}{16}$ pounds