Problema Solution
Four shops in the Mall were having their back-to-back school sale for students. Each student had to pay $0.50 to get into a store and $0.50 to get out. Beau went to the first shop, paid his money to get in, spent ½ the money he had left and then paid $0.50 to leave He went to the second store, paid $0.50 to enter, spent ½ what he had left, and then paid $0.50 to leave. He did the same thing at the third and fourth stores. After paying $0.50 to leave the last shop, he was out of money. How much money did Beau start have when he started shopping?
Answer provided by our tutors
let 'x' represent the amount of money Beau had when he started shopping
let 'x' represent the amount of money Beau has when he enters a store, then the spending pattern Beau followed is:
0.5 + (x-0.5)/2 + 0.5 = 1 + (x-0.5)/2
if we follow the problem backwards, then the money accumulates as:
.50 + 2(x+0.5) + 0.5 = 1+(2x+0.5)
he entered store 4 with: 1 + 2*0 + .5 = 1.50
he entered store 3 with: 1 + 2*1.5 + .5 = 4.50
he entered store 2 with: 1 + 2*4.5 + .5 = 10.50
he entered store 1 with: 1 + 2*10.5 + .5 = 22.50
Beau started shopping with $22.50