Question
Tom had 4 times as much money as Mark at first. After Tom received $400 and Mark received $300, Tom had 3 times as much money as Mark.
a) How much money did Mark have at first?
b) What was the percentage increase in the amount of money Mark had?
a) How much money did Mark have at first?
b) What was the percentage increase in the amount of money Mark had?
Answers
Answered by
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Let's assume Mark had x dollars at first.
Tom had 4 times as much money as Mark at first, so he had 4x dollars.
After Tom received $400, he had 4x + 400 dollars.
After Mark received $300, he had x + 300 dollars.
According to the second statement, Tom had 3 times as much money as Mark after that, so we can write the equation 4x + 400 = 3(x + 300).
Simplifying the equation gives us 4x + 400 = 3x + 900.
Subtracting 3x from both sides gives us 4x - 3x + 400 = 900.
Combining like terms gives us x + 400 = 900.
Subtracting 400 from both sides gives us x = 500.
Therefore, Mark had $500 at first.
The percentage increase in the amount of money Mark had is (300/500)*100 = 60%. Answer: \boxed{60}.
Tom had 4 times as much money as Mark at first, so he had 4x dollars.
After Tom received $400, he had 4x + 400 dollars.
After Mark received $300, he had x + 300 dollars.
According to the second statement, Tom had 3 times as much money as Mark after that, so we can write the equation 4x + 400 = 3(x + 300).
Simplifying the equation gives us 4x + 400 = 3x + 900.
Subtracting 3x from both sides gives us 4x - 3x + 400 = 900.
Combining like terms gives us x + 400 = 900.
Subtracting 400 from both sides gives us x = 500.
Therefore, Mark had $500 at first.
The percentage increase in the amount of money Mark had is (300/500)*100 = 60%. Answer: \boxed{60}.