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Question 1203187: Elvis had $247.60 more than Matthew. Elvis spent 3/8 of his money and Matthew spent 25% of his money. They had $506.75 left altogether.
a) How much money did Matthew have left?
b) How much money did Elvis have at first?
Found 2 solutions by josgarithmetic, papachick24025:
Answer by josgarithmetic(39618)   (Show Source):
Answer by papachick24025(6) (Show Source):
You can put this solution on YOUR website! To find the answers to the given question, we need to set up a system of equations based on the given information.
Let's assume that Matthew had x dollars initially. According to the first statement, Elvis had $247.60 more than Matthew, so Elvis had (x + $247.60) dollars initially.
Next, we are told that Elvis spent 3/8 of his money and Matthew spent 25% of his money. Therefore, after spending, Elvis had (5/8) * (x + $247.60) dollars left, and Matthew had (75/100) * x = (3/4) * x dollars left.
Finally, we are given that they had $506.75 left altogether. So, we can set up the equation:
(5/8) * (x + $247.60) + (3/4) * x = $506.75
To solve this equation, we can simplify it step by step:
Multiply both sides of the equation by 8 to eliminate the fraction:
5(x + $247.60) + 6x = 8 * $506.75
5x + 5 * $247.60 + 6x = $4054
11x + $1238 = $4054
Subtract $1238 from both sides:
11x = $4054 - $1238
11x = $2816
Divide both sides by 11 to solve for x:
x = $2816 / 11
x ≈ $256
Now that we have found the value of x, we can calculate the answers to the questions:
a) How much money did Matthew have left?
Matthew had (3/4) * x = (3/4) * ($256) = $192 left.
b) How much money did Elvis have at first?
Elvis had (x + $247.60) = ($256 + $247.60) = $503.60 at first.
Therefore, Matthew had $192 left, and Elvis had $503.60 at first.
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