Ray saved $240 more money than John. After Ray gave 5/12 of his savings to John, Ray still had $20 more money than John.

Question

a) How much money did Ray have in the end?
b) How much money did John have at first?

Answer 1

Let's start by using algebra to solve the problem.

Let's assume that John had x dollars saved at first. Then, we know from the problem that Ray had $240 more saved than John, so Ray had (x + $240) saved at first.

After Ray gave 5/12 of his savings to John, Ray had 7/12 of his original savings left. We know that this was $20 more than what John had, so we can set up an equation:

7/12(x + $240) = $20 + 5/12x

Now we can solve for x:

7/12x + $140 = $20 + 5/12x

2/12x = $-120

x = $-720

This doesn't make sense as a solution, because it means that John had negative money saved at first. So we made an error somewhere.

Let's try another approach. We know that Ray had $240 more saved than John at first, so we can write:

Ray's savings = John's savings + $240

After Ray gave 5/12 of his savings to John, Ray had 7/12 of his original savings left, so we can write:

7/12(Ray's savings) = John's savings + $20

Now we can substitute the first equation into the second equation:

7/12(John's savings + $240) = John's savings + $20

Simplifying:

7/12 John's savings + $140 = John's savings + $20

6/12 John's savings = $-120

John's savings = $-240

This still doesn't make sense as a solution. We made another mistake.

Let's try one more time. This time, let's start with the second equation and solve for Ray's savings, then use the first equation to solve for John's savings.

7/12(Ray's savings) = John's savings + $20

Ray's savings = 12/7(John's savings + $20)

Ray's savings = 12/7 John's savings + $240/7

Now we can substitute this into the first equation:

12/7 John's savings + $240/7 = John's savings + $240

5/7 John's savings = $240

John's savings = $168

Now we can use the first equation to find Ray's savings:

Ray's savings = $168 + $240

Ray's savings = $408

So the answers are:

a) Ray had $408 in the end.

b) John had $168 at first.