SOLUTION: A man goes to the bank and asks for x dollars and y cents. The banker by mistake gives him y dollars and x cents. After a nickel drops on the floor, the man looks at his money and

Question 863922: A man goes to the bank and asks for x dollars and y cents. The banker by mistake gives him y dollars and x cents. After a nickel drops on the floor, the man looks at his money and realizes that he now has twice the amount he asked for. What was the amount he asked for?
I can only come up with the equation: 2 ( x +.01y) = y + .01x - .05 to reflect this.
I have tried to solve it and can't do it.
Would you please give me some guidance or explain what to do? Is my equation incorrect.
Thank you,
Deborah Aboud
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
You can't solve this by just using mathematics . There are two unknowns and one equation.
2 (x +.01y) = y + .01x - .05
2*(d +.01c) = c + .01d - .05
multiply through by 100
2*(100d +c) = 100c + d- 5
200d+2c=100d+c-5
199d=98c-5
We know that x/d and y/c must be integers.
one solution is
d = 129 and c = 262
general formula for integer solutions
d = 98n+31 and c = 199n+63
$129 and $2.62 in cents
check
2*(12900+262)=26200+129-5
ok
$227 and 461 in cents
2*(22700+461)=46100+227-5
$325 and 660 in cents
2*(32500+660)=66000+325-5

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