Alfred and Charlie have the same amount of money. After Alfred spent 2/7 of his money and Charlie spent $900, Charlie has $300 less than Alfred. How much money does each of them have at first?
A's amount --- x
C's amount --- x
after spending spree:
A had 5/7 x or 5x/7
C had x - 900
A - C = 300
5x/7 - (x-900) = 300
times 7
5x - 7x + 6300 = 2100
-2x = - 4200
x = 2100
each had 2100
1 - 2/7 = 5/7
(5/7) A - 300 = C- 900
but
A = C
(2/7) A = 600
A = C = 300* 7 = 2100
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check
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(5/7) 2100 = 1500 = what A had left
2100 - 900 = 1200 = what C had left
1500 - 1200 = 300 sure enough
To solve this problem, let's set up equations based on the given information:
Let's assume that both Alfred and Charlie have x amount of money initially.
After Alfred spent 2/7 of his money, he would have (1 - 2/7) * x = 5/7 * x left.
We are given that Charlie spent $900, so he would have x - $900 left.
We are also told that Charlie has $300 less than Alfred. Therefore, we can set up an equation:
5/7 * x = x - $900 + $300
To simplify the equation, let's convert the dollars to the same unit (cents, for example):
5/7 * x = x - 90000 + 30000
Now, let's solve the equation step by step:
Multiply both sides of the equation by 7 to get rid of the fraction:
5x = 7x - 90000 + 30000
Subtract 7x from both sides:
-2x = -60000
Divide both sides by -2:
x = 30000
Therefore, each of them initially has $30000.
So, both Alfred and Charlie initially have $30000.