Marlee was given some money to spend on vacation. After spending 1/2 and then losing 1/3 of what was left, he had exactly enough money to pay for some gum and a license plate with his name on it. The license plate was three times the value of the gum, which was $1.76. How much money did Marlee spend on vacation?
To find out how much money Marlee spent on vacation, we need to work backward from the information given.
Let's start by figuring out the cost of the license plate. We know that the license plate was three times the value of the gum, which was $1.76. So, the cost of the license plate is 3 * $1.76 = $5.28.
Since Marlee had exactly enough money to pay for the gum and the license plate after spending 1/2 and losing 1/3 of what was left, we can add the cost of the gum and the license plate to find the total amount of money Marlee had at that point.
The cost of the gum is given as $1.76, and the cost of the license plate is $5.28. Adding them together, we get $1.76 + $5.28 = $7.04.
Now, we know that Marlee had exactly enough money to pay for the gum and the license plate, and this amount represents 2/3 of what was left after spending 1/2.
Let's call the original amount of money Marlee had as "X."
After spending 1/2, Marlee has (1/2) * X left.
After losing 1/3 of what was left, Marlee has (2/3) * [(1/2) * X] left.
According to the information given, this amount is exactly $7.04.
So, we can set up the equation:
(2/3) * [(1/2) * X] = $7.04
Let's simplify the equation:
(2/3) * (1/2) * X = $7.04
Multiplying the fractions:
(1/3) * X = $7.04
Now, we can solve for X by multiplying both sides of the equation by 3:
X = $7.04 * 3 = $21.12
Therefore, the original amount of money Marlee had before spending any on vacation was $21.12.
To find out how much money Marlee spent on vacation, we need to subtract the amount of money Marlee had left after spending 1/2 ($21.12 * (1/2)) from the original amount.
Amount spent on vacation = $21.12 - ($21.12 * (1/2))
= $21.12 - $10.56
= $10.56
So, Marlee spent $10.56 on vacation.