Question

A grapefruit is 8% heavier than an orange, and an apple is 10% lighter than the orange.

a.)By what percentage is the grapefruit heavier than the apple?

b.)By what percentage is the apple lighter than the grapefruit?

Answer 1

weight of an grapefruit=weight of an orange+8% weight of an orange
weight of an apple=weight of an orange -10% weight of an orange

a.By what percentage is the grapefruit heavier than the apple?
We should find the connection between grapefruit and an apple. We know the connection between the weight of a grapefruit and an orange, we know the connection between an orange and an apple, so this means we know the connection between a grapefruit and an apple.

weight of an grapefruit=weight of an orange+8% weight of an orange
weight of an orange=weight of an apple +10% weight of an apple

-> weight of an grapefruit=weight of an apple+10% weight of an apple + 8%(weight of an apple+10% weight of an apple)= weight of an apple + 18% weight of an apple + 2% weight of an apple= weight of an apple + 20% weight of an apple 

b.By what percentage is the apple lighter than the grapefruit?
weight of an grapefruit=weight of an apple + 20% weight of an apple 

-> The apple ts 20% lighter than the grapefruit.

Answer 2

a.) The grapefruit is 20 percent heavier than the apple.

b.) The apple is 16.67 percent lighter than the grapefruit.

What are percentages?

A percentage is a quantity or ratio represented as a fraction of one hundred. Divide the number by the total and multiply by 100 if we need to determine the percent of a number. As a result, the percentage denotes a part per hundred. The word per-cent means per 100.

How do we solve the given question?

We are given that grapefruit is 8% heavier than an orange, and an apple is 10% lighter than an orange.

Let the weight of the orange be x.

∴ Weight of grapefruit = x + 8% of x

or, Weight of grapefruit = x + (8/100) * x = x + 0.08x = 1.08x.

∴ Weight of apple = x - 10% of x

or, Weight of apple = x - (10/100) * x = x - 0.1x = 0.9x.

a.) We are asked to tell, by what percentage is the grapefruit heavier than the apple.

Difference in weights of grapefruit and apple = 1.08x - 0.9x= 0.18x

∴ Percentage grapefruit is heavier = (0.18x/0.9x)*100% = 100/5% = 20%.

∴ The grapefruit is 20% heavier than the apple.

b.) We are asked to tell, by what percentage is the apple lighter than the grapefruit.

Difference in weights of grapefruit and apple = 1.08x - 0.9x= 0.18x

∴ Percentage apple is lighter = (0.18x/1.08x)*100% = 100/6%=16.67%.

∴ The apple is 16.67% lighter than the grapefruit.

Learn more about the Percentages at

https://brainly.com/question/843074

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