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?
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}.
Let's solve this step by step.
a) Let's first set up the equations based on the given information:
Tom had 4 times as much money as Mark at first: T = 4M, where T represents Tom's money and M represents Mark's money.
After Tom received $400 and Mark received $300, Tom had 3 times as much money as Mark: (T + 400) = 3(M + 300).
Now, let's substitute the value of T from the first equation into the second equation:
(4M + 400) = 3(M + 300).
Expanding the equation:
4M + 400 = 3M + 900.
Combining like terms:
4M - 3M = 900 - 400,
M = 500.
Therefore, Mark had $500 at first.
b) To calculate the percentage increase in the amount of money Mark had, we need to find the difference between the initial and final amounts and then calculate the percentage increase.
The initial amount Mark had was $500, and after receiving $300, the final amount Mark had is $500 + $300 = $800.
The difference in the amount Mark had is $800 - $500 = $300.
To calculate the percentage increase, we use the formula: (difference / initial amount) * 100.
Percentage increase = (300 / 500) * 100 = 60%.
Therefore, the percentage increase in the amount of money Mark had is 60%.