The Mall: My sister likes to go shopping. Yesterday she borrowed a wad of money from Mom and went to the mall. She began her excursion by spending $18 on a new CD. Then she spent half her remaining money on a new dress. Then she spent $11 on lunch. Then she spent one-third of her remaining money on a book. On her way home she bought gas for $12 and spent one-fourth of the remaining money on a discounted CD at the convience store. Finally, she slipped me $2 when she got home, and gave mom $10 in change. Mom was furious and demanded an explanation of where the money went. List the items she bought and the amount spent on each item and tell how much she started with."

I think the answer is $124 but i'm not sure...

too bad you couldn't be bothered to show your work.

start: $x
CD: 18, leaving x-18
dress: half that, leaving x/2 - 9
lunch:11, leaving x/2 - 20
book: 1/3 of that, leaving (2/3)(x/2-20) = x/3 - 40/3
gas: 12, leaving x/3 - 76/3
CD: 1/4 of that, leaving (3/4)(x/3 - 76/3) = x/4 - 19
slipped 2, leaving x/4 - 21

so, x/4 - 21 = 10
x = 124

Good work.

start with x dollars and go through the steps

after CD's : x-18
spend 1/2 of that, leaving (x-18)/2
after lunch, amount left = (x-18)/2 - 11
spends 1/3 of that on book leaving with
(2/3)( (x-18)/2 - 11), let's simplify that a bit
= (2/3)(x/2 - 9 - 11)
= (2/3)(x/2 - 20)
= x/3 - 40/3

spent 12 on gas, leaving her with x/3 - 40/3 - 12
= x/3 - 76/3
spent 1/4 of that on another CD
leaving her with (3/4)(x/3 - 76/3)
= x/4 - 19
gave another $2 away leaving her with $10
x/4 - 21 = 10
x/4 = 31
x = 124 , yeah you were right.

check:
start with 124, spend 18 on CD's , left with 106
spend half of that on dress, leaving 53
after lunch , left with 42
1/3 of that on book , leaving (2/3)of 42 or 28
bought gas of $12, leaving $16
spent 1/4 of 16 on another CD, leaving 12
after slipping you $2, amount left is $10.

Well, it seems like your sister had quite an eventful shopping trip! Let's break down the expenses to find out where her money went.

1. CD: She spent $18.
2. Dress: She spent half of her remaining money, which means she spent $18 / 2 = $9 on the dress.
3. Lunch: She spent $11.
4. Book: She spent one-third of her remaining money, so she spent ($124 - $18 - $9 - $11) / 3 = $28 / 3 ≈ $9.33 on the book.
5. Gas: She spent $12.
6. Discounted CD: She spent one-fourth of her remaining money, which means she spent ($124 - $18 - $9 - $11 - $9.33 - $12) / 4 ≈ $14.42 / 4 ≈ $3.61 on the discounted CD.
7. She gave you $2 and gave Mom $10 in change.

To find out how much money she started with, let's add up all the expenses and the money she gave you and Mom:
$18 + $9 + $11 + $9.33 + $12 + $3.61 + $2 + $10 = $74.94.

So it appears that your sister started with $74.94, not $124. Oops! Looks like she went a bit overboard with her shopping.

To find out how much your sister started with and the items she bought, we can follow these steps:

1. Let's start by calculating the total amount your sister spent.

- She spent $18 on a new CD.
- Then, she spent half of her remaining money on a new dress.
- After that, she spent $11 on lunch.
- Then, she spent one-third of her remaining money on a book.
- Next, she bought gas for $12.
- She spent one-fourth of her remaining money on a discounted CD at the convenience store.
- Finally, she gave you $2 and gave mom $10 in change.

So far, the total amount spent can be calculated as:
$18 + (1/2)R + $11 + (1/3)(R - $18 - (1/2)R - $11) + $12 + (1/4)(R - $18 - (1/2)R - $11 - (1/3)(R - $18 - (1/2)R - $11)) + $2 + $10 = Total spent.

2. Now, let's solve for R (the amount she started with) using the total amount spent:

Total spent = R - Remaining money

Total spent = R - ($18 + (1/2)R + $11 + (1/3)(R - $18 - (1/2)R - $11) + $12 + (1/4)(R - $18 - (1/2)R - $11 - (1/3)(R - $18 - (1/2)R - $11)) + $2 + $10)

We can simplify this equation to find the value of R.

3. Once we have found the value of R, we can calculate how much she spent on each item.

- $18 on a new CD.
- Half of the remaining money on a new dress.
- $11 on lunch.
- One-third of the remaining money on a book.
- $12 on gas.
- One-fourth of the remaining money on a discounted CD.
- $2 given to you.
- $10 given to mom as change.

Please note that since there is no specific rate provided for half, one-third, or one-fourth of the remaining money, we cannot calculate the exact amounts spent on the new dress, book, and discounted CD. However, we can calculate the proportions and express them as a ratio of the remaining money.

To find out how much money your sister started with and the amount spent on each item, let's break down the information step by step.

1. Your sister began by spending $18 on a new CD.
Remaining money: Initial amount - $18 = Initial amount.

2. She then spent half of her remaining money on a new dress.
Remaining money: Initial amount - $18 - (1/2 * Initial amount).

3. She spent $11 on lunch.
Remaining money: Initial amount - $18 - (1/2 * Initial amount) - $11.

4. Next, she spent one-third of her remaining money on a book.
Remaining money: Initial amount - $18 - (1/2 * Initial amount) - $11 - (1/3 * (Initial amount - $18 - (1/2 * Initial amount) - $11)).

5. She bought gas for $12.
Remaining money: Initial amount - $18 - (1/2 * Initial amount) - $11 - (1/3 * (Initial amount - $18 - (1/2 * Initial amount) - $11)) - $12.

6. She spent one-fourth of the remaining money on a discounted CD at the convenience store.
Remaining money: Initial amount - $18 - (1/2 * Initial amount) - $11 - (1/3 * (Initial amount - $18 - (1/2 * Initial amount) - $11)) - $12 - (1/4 * (Initial amount - $18 - (1/2 * Initial amount) - $11 - $12)).

7. Finally, she slipped you $2 and gave Mom $10 in change.
Remaining money: Initial amount - $18 - (1/2 * Initial amount) - $11 - (1/3 * (Initial amount - $18 - (1/2 * Initial amount) - $11)) - $12 - (1/4 * (Initial amount - $18 - (1/2 * Initial amount) - $11 - $12)) - $2 - $10.

By simplifying the above expression, you can determine the actual amount she started with and how much was spent on each item.