Question

In February, Dawn's monthly allowance and Evelyn's monthly allowance were in the ratio 5: 8. In March, Mother increased Dawn's monthly allowance by 20% and decreased Evelyn's monthly allowance. Dawn and Evelyn then had the same amount of allowance. What was the percentage decrease in Evelyn's allowance in March?​

Answer 1

25%

Explanation:

Let Dawn’s monthly allowance be 5x. Let Evelyn’s monthly allowance then be 8x.

Percentage increase by 20% is the same as multiplying a number by 1.2

To find the percentage decrease of Evelyn’s monthly allowance, we can equate their allowances after the change of their initial allowance.

1.2 * 5x = k/100 * 8x

k represents the percentage

6x = 8xk/100

Cancel the x’s from both sides

6 = 8k/100

600 = 8k

k = 75

Therefore since 75% of Evelyn’s monthly allowance is equal to Dawn’s increased monthly allowance, this means Evelyn’s monthly allowance was decreased by 25%.