Question

Victoria spent all her money in five stores. In each store, she spent $1 more than half of what she had when she came in. How much did Victoria have when she entered the first store?

Answer 1

store #1
came in with x
spent x/2 + 1 = (x+2)/2
amount left = x - (x+2)/2 = (2x - x - 2)/2 = (x-2)/2

store #2
came in with (x-2)/2
spent (1/2)(x-2)/2 + 1
= x/4 - 1/2 + 1 = x/4 + 1/2 = (x+2)/4
amount left = (x-2)/2 - (x+2)/4
= (2x - 4 - x - 2)/4 = (x - 6)/4

Store #3
came in with (x-6)/4
spent (1/2)(x-6)/4 + 1
= (x-6)/8 + 1 = (x - 6 + 8)/8 = (x + 2)/8
amount left = (x-6)/4 - (x+2)/8
= (2x - 12 - x - 2)/8 = (x - 14)/8

carry on with #4 and #5
when you have calculated "amount left at end of store #5", set that equal to zero
and solve for x

Test your answer by doing the steps.