This question I have

Question

If I give my sister $7, then we will have the same amount of money.  If, instead, she gives me $8, then I'll have twice as much money she has. How much money does she have? 

Answer 1

Hello, Batty.

Okay, so if you give your sister $7, then you will have the same amount of money.

Let's call the amount of money she has, X and the amount you have Y.

So,:if you give her $7, you will have Y - 7 and she will have X + 7. Also, if you give her the $7,

you will have the same amount of money. So:

Y - 7 = X + 7

Also, if she gives you $8, then you will have twice as much money as her. This would mean:

She would then have X - 8 dollars and you would have Y + 8 dollars . Also, if that happens, you will have twice as much money as she does. So

2(X - 8) = Y + 8

So now we need to solve these equations:

Y - 7 = X + 7

2(X - 8) = Y + 8

Let's use substitution to solve these. If we solve the first equation for we have:

Y = X + 14

Now, we can substitute X + 14 for Y in the 2nd equation

2(X - 8) = (X + 14) + 8

2X - 16 = X + 22

X = 38

So, your sister has $38.

Let's plug it into the original equations to check our answer:

Y - 7 = X + 7

Y - 7 = 38 + 7

Y = 52

Now check the 2nd equation:

2(X - 8 ) = Y + 8

2(38 - 8) = 52 + 8

2x30 = 60

60 = 60

The solution is correct.

Your sister has $38 and you have $52