April, May and June are counting up the money they've saved from their weekly allowance. May has 20% less than April, and June has 20% more than May. Together, the three girls have $138. How much money
does each girl have?

Answers:

April = $50May = $40June = $48

Work Shown:

x = amount April has

0.80x = amount May has

1.20*0.80x = 0.96x = amount June has

The sum of the three amounts adds to 138

(april) + (may) + (june) = 138

(x) + (0.80x) + (0.96x) = 138

2.76x = 138

x = 138/2.76

x = 50 is the amount April has

0.80x = 0.80*50 = 40 is the amount May has

0.96x = 0.96*50 = 48 is the amount June has

As a check, 50+40+48 = 90+48 = 138 to verify the answer.

Side notes:

Since May has 20% less than April, this means May has 80% of April's amount, which is where the 0.80 comes from in 0.80x; put another way, decreasing by 20% means we use the multiplier 0.80Increasing by 20% means we use the multiplier 1.2048/40 = 1.20Decreasing by 20% and then increasing by 20% will not lead you back to the original value (since we go from 50 to 40 then up to 48). This is because we're increasing by a smaller amount compared to the amount decreased earlier, i.e. 20% of a smaller value is smaller overall.

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