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The ratio of Noah to William's savings was 2 : 3 at first. After Noah saved another $124 and William saved another $48, Noah had twice of William. How much did Noah have in the end?

Question

The ratio of Noah to William's savings was 2 : 3 at first. After Noah saved another 124andWilliamsavedanother124 and William saved another 48, Noah had twice of William. How much did Noah have in the end?

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Solution

Let's denote the initial amount of money Noah had as 2x and the initial amount William had as 3x.

According to the problem, after Noah saved another 124andWilliamsavedanother124 and William saved another 48, Noah had twice as much as William. This can be written as:

2x + 124 = 2 * (3x + 48)

Solving this equation will give us the value of x. Let's do it:

First, distribute the 2 on the right side of the equation:

2x + 124 = 6x + 96

Then, subtract 2x from both sides:

124 = 4x + 96

Next, subtract 96 from both sides:

28 = 4x

Finally, divide both sides by 4 to solve for x:

x = 7

Now that we know x = 7, we can find out how much money Noah had in the end. We know that Noah initially had 2x, and he saved another $124. So, the total amount of money Noah had in the end is:

2x + 124 = 2*7 + 124 = $138.

This problem has been solved

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