Claire has a sum of money. She spent $50 on a dress and 4 7 of the remainder on a book. She was left with 1 4 of the original sum of money. How much money did Claire have at first?
Let X be the original sum of money Claire had.
She spent 1/4*X + 50 on the dress and the book, leaving her with X - 1/4*X - 50 = 3/4*X - 50
So she spent 4/7 * (3/4*X - 50) = 0.42857 * (3/4*X - 50) = 0.42857 * 3/4 * X - 0.42857 * 50 = 1/14 * X - 0.42857 * 50 on the book.
The remainder was X - 1/4*X - 50 - 1/14 * X + 0.42857 * 50 = 1/2*X - 50 + 21.42857 = 1/2*X - 28.57143
So, 1/2*X - 28.57143 = 1/4*X
So, 2/2*X - 28.57143 = 1/4*X
So, 2/2*X - 1/4*X = 28.57143
So, 7/4*X = 28.57143
So, X = 28.57143 * 4 / 7 = <<28.57143*4/7=16.326530612244903>>16.326530612244903 dollars. Answer: \boxed{16.326530612244903}.
Let's assume that the original sum of money that Claire had is represented by "x".
According to the given information:
1. Claire spent $50 on a dress, so the remaining amount of money is (x - 50).
2. She then spent 4/7 of the remainder on a book, which means she spent (4/7)*(x - 50) on the book.
3. After these expenses, she was left with 1/4 of the original sum of money, which is (1/4)*x.
Based on the above information, we can create the equation:
(4/7)*(x - 50) = (1/4)*x
To solve this equation, we can start by multiplying both sides by 28 to eliminate the denominators:
4*(x - 50) = 7*(1/4)*x
Simplifying, we get:
4x - 200 = 7/4 * x
Now let's isolate the variable by subtracting 7/4 * x from both sides:
4x - 7/4 * x = 200
Multiplying both sides by 4 to clear the fraction:
16x - 7x = 800
Simplifying further:
9x = 800
Finally, divide both sides by 9:
x = 800 / 9
Therefore, the original sum of money that Claire had was approximately $88.89.
To find out how much money Claire had at first, we need to work through the problem step by step.
Let's assume the amount of money Claire had at first is represented by the variable "x".
According to the problem, Claire spent $50 on a dress. This means she had "x - 50" dollars remaining.
Next, Claire spent 4/7 of the remaining money on a book. This can be represented as (4/7) * (x - 50) dollars. After buying the book, Claire was left with 1/4 of the original sum of money, which can be represented as (1/4) * x dollars.
Now let's set up an equation to find x:
(x - 50) - (4/7) * (x - 50) = (1/4) * x
To solve this equation, we can simplify both sides:
x - 50 - (4/7) * x + (4/7) * 50 = (1/4) * x
Multiplying fractions:
x - 50 - (4/7) * x + (200/7) = (1/4) * x
Next, we can simplify the equation by getting rid of the fractions:
Multiply every term by the least common denominator, which is 28.
28x - 1400 - 16x + 800 = 7x
Combine like terms:
12x - 600 = 7x
Subtract 7x from both sides:
12x - 7x - 600 = 0
5x - 600 = 0
Add 600 to both sides:
5x = 600
Divide by 5:
x = 120
Therefore, Claire had $120 at first.