Question

Lynne 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 weigh

Answer 1

`\text{Weight of grape fruit is } 3.6875 \text{ or } (59)/(16) \text{ or } 3(11)/(16) \text{ pounds }`

Solution:

Given that,

Pound of apples =
`1(5)/(8)`

Pounds of bananas =
`2(3)/(16)`

Total weight =
`7(1)/(12)`

Let us first convert the mixed fractions to improper fractions

Multiply the whole number part by the fraction's denominator.

Add that to the numerator.

Then write the result on top of the denominator.

Therefore,

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

Thus we get,

`Pounds\ of\ apples = (13)/(8)\\\\pounds\ of\ bananas = (35)/(16)\\\\total\ weight = (15)/(2)`

Now to find weight of grape weight use the following formula

Weight of grape fruit = total weight - (pounds of apples + pounds of bananas)

`\rightarrow (15)/(2) - ((13)/(8) + (35)/(16))\\\\\rightarrow (15)/(2) - ((13 * 2)/(8 * 2) + (35)/(16))\\\\\rightarrow (15)/(2) - ((26)/(16) + (35)/(16))\\\\\rightarrow (15)/(2) - (61)/(16)`

Now make the denominators same for easier calculations

`\rightarrow (15 * 8)/(2 * 8) - (61)/(16)\\\\\rightarrow (120)/(16) - (61)/(16)\\\\\rightarrow (120-61)/(16) = (59)/(16)`

Again in mixed fractions we get,

`\rightarrow (59)/(16) = 3(11)/(16)`

In decimal form we get,

`\rightarrow (59)/(16) = 3.6875`

Thus weight of grape fruit is
`3.6875 \text{ or } (59)/(16) \text{ or } 3(11)/(16)` pounds