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?
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.
To find out how much Victoria had when she entered the first store, we can solve this problem step by step.
Let's start by assigning a variable to the amount of money Victoria had when she entered the first store. Let's call it "x".
According to the problem, in each store, Victoria spent $1 more than half of what she had when she came in. So, in the first store, she spent (1/2)x + $1.
After leaving the first store, Victoria had (x - [(1/2)x + $1]) dollars left.
Now, she goes to the second store with the remaining money from the first store and spends (1/2) times that amount plus $1 again. So, in the second store, she spends (1/2)(x - [(1/2)x + $1]) + $1.
We can continue this process for all five stores, subtracting the amount she spent from the remaining money each time.
Finally, after leaving the fifth store, Victoria has no money left.
By setting up and solving this equation, we can determine the initial amount she had when she entered the first store:
x - [(1/2)(x - [(1/2)(x - [(1/2)(x - [(1/2)x + $1]) + $1]) + $1]) + $1]) = $0
Simplifying and solving this equation will give us the amount of money Victoria had when she entered the first store.