laura spent 20 percent of her money on a dress. she spent 2/5 of the remainder on a book. she had $72 left. how much money did she have at first?
Oh, Laura and her shopping adventures! Let's do some math and solve this riddle.
Let's start with x as the amount of money Laura had initially. According to the problem, she spent 20% of her money on a dress, which leaves her with 80% of her money. So, she had 0.80x left.
Now, she spends 2/5 of that remaining money on a book. That means she spent (2/5) * 0.80x = 0.32x on the book.
After purchasing the book, Laura has $72 left. So, we can set up the equation: 0.80x - 0.32x = $72.
Let's solve it using some mathematical magic:
0.80x - 0.32x = 72
0.48x = 72
x = 72 / 0.48
x = $150
So, Laura had $150 at first! Now she can go shopping again and I can hear her wallet crying tears of joy.
Let's assume Laura had x dollars at first.
Step 1: Laura spent 20% of her money on a dress.
This means she spent 0.20x dollars on the dress.
So, she had (x - 0.20x) dollars left after buying the dress, which simplifies to 0.80x dollars.
Step 2: Laura spent 2/5 of the remainder on a book.
This means she spent (2/5)(0.80x) dollars on the book.
So, she had (0.80x - (2/5)(0.80x)) dollars left after buying the book, which simplifies to (0.80x - 0.32x) dollars.
Step 3: Laura had $72 left.
According to the given information, (0.80x - 0.32x) = 72 dollars.
Step 4: Solve for x.
Combine like terms: 0.48x = 72.
Divide both sides by 0.48: x = 72 / 0.48.
x ≈ 150.
Therefore, Laura had approximately $150 at first.
To find out how much money Laura had at first, we can follow these steps:
1. Let's assume Laura's initial amount of money is represented by 'x' dollars.
2. Laura spent 20 percent of her money on a dress, which can be calculated by multiplying 'x' by 20/100 or simply by multiplying 'x' by 0.2. This amount is subtracted from her initial money, so she has (x - 0.2x) dollars remaining.
3. Laura then spent 2/5 of the remainder on a book. To calculate this, multiply (x - 0.2x) by 2/5 or by 0.4. So, she spent 0.4(x - 0.2x) dollars on a book.
4. Subtract the money spent on the book from the remaining money (x - 0.2x) to find out how much money she has left. This is equal to (x - 0.2x) - 0.4(x - 0.2x), which simplifies to (0.8x - 0.4x).
5. We are given that she has $72 left, so we can set up the equation (0.8x - 0.4x) = 72 and solve it.
Let's calculate it step by step:
0.8x - 0.4x = 72
0.4x = 72
x = 72 / 0.4
x = 180
Therefore, Laura had $180 at first.
after dress she has 4/5 of her money left
after book would have left (3/5)(4/5) or 12/25 of her money left
so (12/25)x = 72
x = 150
I will leave it up to your to check my answer