Question

Carmen received some money for her birthday on Friday. That night, she took her friend out to dinner. She spent half of her check for dinner. Then she tipped the waiter $6. The next evening she went to dinner alone, spent half of the money she had left, and tipped the waiter $2. The next night she went to dinner again, spent half of the money she had left, and tipped the waiter $1. At this time she had $6 left. How much money did she originally have?

Answer 1

First Trip

Check = X dollars.
Spent: X/2 + 6,
BAL = X - (X/2 + 6) = X/2 - 6.

SECOND TRIP

Spent: 1/2(X/2 - 6) + 2 = X/4 - 1.
BAL = (X/2 - 6) - (X/4 - 1) = X/4 - 5.

THIRD TRIP

Spent: 1/2(X/4 - 5) = X/8 - 5/2.
BAL=(X/4 - 5) - (X/8 - 5/2) = X/8 - 5/2

X/8 - 5/2 = 6,
Multiply both sides by 8:
X - 20 = 48,
X=48 + 20 = $68 = The original amount.

Answer 2

72