Natalie had a sum of money. She spent $50 on a dress and 4/7 of the remainder on a book. She has left with 1/4 of the original sum of money. How much money did Natalie has at first.
Pls help
Well, let's think about this. If Natalie has 1/4 of her original sum of money left, that means she has spent 3/4 of her money. And we know that she spent $50 on a dress and 4/7 of the remainder on a book. So, if we add these together, we get:
3/4 of the original sum = $50 + (4/7 of the remainder)
Now, if we simplify, we can say:
3/4 of the original sum = $50 + (4/7) * (1/4 of the original sum)
Hmm, math isn't great for jokes, is it? Maybe it should stick to comedy clubs.
Let's assume that the original sum of money Natalie had is "x".
After spending $50 on a dress, the remainder of her money is "x - $50".
She then spent 4/7 of the remainder on a book, which is (4/7) * (x - $50).
So, the amount of money she has left is 1/4 of the original sum, which is (1/4) * x.
Now, we can set up the equation based on the given information:
(x - $50) - (4/7) * (x - $50) = (1/4) * x
Let's solve this equation step-by-step:
1. Distribute the (4/7) to (x - $50):
x - $50 - (4/7)x + (4/7) * $50 = (1/4) * x
2. Simplify the expressions:
x - $50 - (4/7)x + $20 = (1/4) * x
3. Combine like terms:
(x - (4/7)x) - $50 + $20 = (1/4) * x
4. Continue simplifying:
(3/7)x - $30 = (1/4) * x
5. Multiply both sides by the LCD (28) to eliminate the fractions:
28 * (3/7)x - 28 * $30 = 28 * (1/4) * x
6. Simplify the expressions:
12x - 840 = 7x
7. Subtract 7x from both sides to isolate the x-term:
12x - 7x - 840 = 0
8. Combine like terms:
5x - 840 = 0
9. Add 840 to both sides:
5x = 840
10. Divide both sides by 5 to solve for x:
x = 840/5
11. Simplify the expression:
x = 168
So, the initial sum of money Natalie had is $168.
To find out how much money Natalie had initially, we will use a step-by-step approach.
Step 1: Calculate the amount Natalie spent on the dress.
Natalie spent $50 on the dress.
Step 2: Find the remainder after buying the dress.
The remainder will be the initial sum of money minus the amount spent on the dress.
Let's represent the initial sum of money as "x."
Remaining money = x - $50.
Step 3: Calculate the amount spent on the book.
Natalie spent 4/7 of the remainder on a book.
Amount spent on the book = (4/7) * Remaining money.
Step 4: Calculate the remaining money after buying the book.
Remaining money = Remaining money - Amount spent on the book.
Remaining money = Remaining money - (4/7) * Remaining money.
Step 5: Calculate the fraction of the original sum of money that is left.
Natalie has 1/4 of the original sum of money left.
1/4 of the original sum of money = (1/4) * x.
Step 6: Set up an equation using the information from Step 4 and Step 5.
(1/4) * x = Remaining money.
1/4 * x = Remaining money - (4/7) * Remaining money.
Step 7: Simplify the equation.
Multiply both sides of the equation by 4 to eliminate the fraction.
x = 4 * (Remaining money - (4/7) * Remaining money).
x = 4 * (Remaining money - (4/7) * Remaining money).
x = 4 * Remaining money - (16/7) * Remaining money.
Step 8: Combine like terms.
x = (28/7) * Remaining money - (16/7) * Remaining money.
x = (28 - 16)/7 * Remaining money.
x = 12/7 * Remaining money.
Step 9: Simplify.
Since Natalie has 1/4 of the original sum of money left, the remaining money is 1/4 * x.
Substitute this value into the equation from Step 8 for Remaining money.
x = 12/7 * (1/4 * x).
x = 12/28 * x.
Step 10: Solve for x.
Multiply both sides of the equation by 28 to eliminate the fraction.
28x = 12x.
16x = 0.
x = 0.
Therefore, Natalie started with $0, which means she had no money initially.