Shiela spent $120 on a coat. She spent 2/3 of her remaining money on a dress. She's left with 1/5 of her money. How much he money did she have to begin with?
(x-120) * (1 - 2/3) = 1/5 x
x = 300
check:
300-120 = 180
2/3 of 180 = 120, leaving 60
50 is 1/5 of 300
Answer:
The answer is 280. 280-120=160 160/4=40 so 40 x 7 = 280
Let's solve the problem step-by-step:
Step 1: Calculate the amount Sheila spent on the coat.
- She spent $120 on the coat.
Step 2: Calculate Sheila's remaining money after buying the coat.
- Let's assume Sheila's remaining money after buying the coat is represented by "x".
- She spent $120 on the coat, so her remaining money is x - $120.
Step 3: Calculate the amount Sheila spent on the dress.
- Sheila spent 2/3 of her remaining money on the dress.
- This can be represented as 2/3 * (x - $120).
Step 4: Calculate Sheila's money remaining after buying the dress.
- Sheila's remaining money after buying the dress is given by [x - $120] - [2/3 * (x - $120)].
Step 5: Calculate the amount Sheila has left.
- The problem states that Sheila is left with 1/5 of her money.
- This can be represented as 1/5 * [x - $120 - 2/3 * (x - $120)].
Step 6: Solve for x.
- Equate the remaining money to 1/5 of her money and solve the equation:
1/5 * [x - $120 - 2/3 * (x - $120)] = x.
1/5 * [3x/3 - $120 - 2(x/3 - $120/3)] = x.
1/5 * [3x/3 - $120 - 2x/3 + $240/3] = x.
1/5 * [x/3 + $120/3] = x.
1/5 * (x + $120) = x.
1/5 * x + 1/5 * $120 = x.
x/5 + $24 = x.
$24 = x - x/5.
$24 = (5x - x)/5.
$24 = 4x/5.
4x = $24 * 5.
4x = $120.
x = $120 / 4.
x = $30.
Therefore, Sheila had $30 to begin with.
To find out how much money Shiela had to begin with, we need to work backwards. Let's break down the problem step by step:
1. Shiela spent $120 on a coat.
2. After buying the coat, she has 2/3 of her remaining money left.
3. She is left with 1/5 of her money.
Let's assign variables for each step to solve this problem systematically.
Step 1: Shiela spent $120 on a coat.
Let's say the amount of money Shiela had before buying the coat was "x."
After buying the coat, she is left with "x - 120" dollars.
Step 2: She spent 2/3 of her remaining money on a dress.
The remaining money after buying the coat is "x - 120" dollars.
She spent 2/3 of this remaining money, so the amount spent on the dress is (2/3)(x - 120) dollars.
The money remaining after buying the dress will be (x - 120) - (2/3)(x - 120) dollars.
Step 3: She is left with 1/5 of her money.
The money remaining after buying the dress is (x - 120) - (2/3)(x - 120) dollars.
According to the problem, this remaining money is 1/5 of her original money.
So we can set up the equation: (x - 120) - (2/3)(x - 120) = (1/5)x.
Now, we can solve this equation to find the value of "x," which represents the amount of money Shiela had to begin with.
Calculating step by step:
Multiply through by 15 to clear the fractions: 15(x - 120) - 10(x - 120) = 3x.
Distribute: 15x - 1800 - 10x + 1200 = 3x.
Combine like terms: 5x - 600 = 3x.
Subtract 3x from both sides: 5x - 3x - 600 = 0.
Simplify: 2x - 600 = 0.
Add 600 to both sides: 2x = 600.
Divide both sides by 2: x = 300.
Therefore, Shiela initially had $300.