My Father went shopping with a sum of money. He spent 1/2 of her money plus 50 pesos on a belt. He then spent 1/2 of the remaining money plus 30 pesos on a pair of sandals. Finally he spent 1/5 of what was left plus 20 pesos on a T-shirt . He was left with 15 pesos. How much money did my Father have at first

2 answers

let Dad start with x
belt: x/2 + 50
amount left = x - (x/2 + 50) = x/2 - 50
sandals: (1/2)(x/2 - 50) + 30 = x/4 + 5
amount left = x/2 - 50 - (x/4 + 5) = x/4 - 55
T-shirt: (1/5)(x/4 - 55) + 20 = x/20 + 9

x/4 - 55 - (x/20 + 9) = 15
x/4 - 55 - x/20 - 9 = 15
x/5 = 79
x = 395 pesos
Try working backwards. We have 15 pesos left. Add 20 and multiply by 5/4,we get 43.75. Add 30, and multiply by 2, we get 147.50. Add 50, and multiply by 2 we get 395 as the amount started with