Question

Alice had $4.80 left after spending 40 percent of her money on lunch, 20 percent of what was left after lunch on parking, and 50 percent of what was left at a café. How much money did Alice have before lunch?

Answer 1

$20

Explanation:

We are given the percentages of how much she spent on each purchase but we need the percentage of what is left after each purchase. We calculate this by subtracting each percentage from 100% like so.

100% - 40% = 60%

100% - 20% = 80%

100% - 50% = 50%

Next we need to do is change the percentages into decimal format. We do this by moving the decimal 2 digits to the left. Therefore the percentages wasted are the following

60.0% ⇔ 0.60

80.0% ⇔ 0.80

50.0% ⇔ 0.50

Now that we have the percentages in decimal format we can calculate the total price (t) by retracing the spending process. The spending process was following.

`t_(2) = 0.60t`

`t_(3) = 0.80t_(2)`

`4.80 = 0.50t_(3)`

So we have to retrace by solving for
`t_(3)`, then
`t_(2)`, and finally (t)

`4.80 = 0.50t_(3)` ... divide both sides by 0.50

`9.60 = t_(3)`

`9.60 = 0.80t_(2)` .... divide both sides by 0.20

`12 = t_(2)`

`12 = 0.60t` .... divide both sides by 0.60

`20 = t`

Finally we can see that the Total amount of money that Alice had before lunch was $20