SOLUTION: If shelly gives John $5, they will have the same amount of money, If John gives shelly $5, she will have twice as much money as he will have. How much money does each have?

Question 572054: If shelly gives John $5, they will have the same amount of money, If John gives shelly $5, she will have twice as much money as he will have. How much money does each have?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = the amount of money that shelly has.
let y = the amount of money that john has.

if shelly give john 5 dollars, then they both have the same amount of money.
this leads to the equation:
x-5 = y+5

if john give shelly 5 dollars, then shelly has twice as much money as john has.
this leads to the equation:
x+5 = 2(y-5)

solve for x in each equation to get:

x-5 = y+5 leads to:
x = y+10

x+5 = 2(y-5) leads to:
x+5 = 2y-10 which becomes:
x = 2y-15

you have 2 expressions that are equal to x.
they are:
x = y+10
x = 2y-15

you can set these expressions equal to each other to get:
y+10 = 2y-15
subtract y from both sides of this equation and add 15 to both sides of this equation to get:
y = 25

since x = 2y-15, this leads to:
x = 2(25)-15 which becomes:
x = 35

the equation x = y + 10 leads to the same answer of:
y =35

you have:
x = 25
y = 35

shelly has 35 dollars and john has 25 dollars.
shelly gives john 5 dollars so shelly has 30 and john has 20 meaning:
shelly and john have the same amount of money.

shelly has 35 dollars and john has 25 dollars.
john give shelly 5 dollars and shelly has 40 and john has 20 meaning:
shelly has twice as much money as john.

the problem has been satisfied so the answer is:
shelly has 35 dollas.
john has 25.

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