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.

Question

a) How much money did Mark have at first?
b) What was the percentage increase in the amount of money Mark had?

Answer 1

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}.