Question

Ben had 3x as much money as Colin. After Ben spent $110 and Colin spent $30, they had the same amount of money left.(a) How much did Colin have at first?(b) How much had each of them left in the end?​

Answer 1

Initially, Colin had $40. After spending their money, both Ben and Colin had $10 left.

Step-by-step explanation:

To solve this problem, we'll set up two equations based on the given information.

Let x represent the amount of money Colin had at first. Since Ben had 3 times as much money as Colin, Ben had 3x dollars. After spending, Ben has 3x - 110 dollars left, and Colin has x - 30 dollars left. According to the problem, they both have the same amount of money after spending, so we can set up the following equation:

3x - 110 = x - 30

Subtract x from both sides:

2x - 110 = -30

Now, add 110 to both sides to solve for x:

2x = 80

Divide by 2:

x = 40

So, Colin had $40 at first. Using this value, we can find out how much each had left in the end:

Ben had 3x - 110 = 3(40) - 110 = 120 - 110 = $10.

And Colin had x - 30 = 40 - 30 = $10.

Therefore, both had $10 left after spending their money.