Dating Twist

Algebra Level 3

Alberto and Betty went out for lunch. Originally, Alberto had more money than Betty did by 20%.

After Alberto and Betty spent $37 and $18, respectively, Betty has more money than Alberto does by 20%.

How much money in total do they have left after lunch?


The answer is 77.

Worranat Pakornrat by Worranat Pakornrat , 36, Thailand

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1 solution

Let A = Alberto's money and B= Betty's money.

1.2 = 6 5 = A B = B − 18 A − 37 1.2 = \dfrac{6}{5} = \dfrac{A}{B} = \dfrac{B-18}{A-37}

Suppose A = 6 x A =6x and B = 5 x B=5x for some x.

Then 6 ( 6 x − 37 ) = 5 ( 5 x − 18 ) 6(6x-37)=5(5x-18) .

36 x − 222 = 25 x − 90 36x-222=25x-90

11 x = 132 11x=132 ; x = 12 x=12 .

The remaining money = 132 − 37 − 18 = 77 132-37-18 = \boxed{77} .

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