bank teller word problem

[CMouser]

:roll: I have a word problem i just cannot get . any help wpuld be appreciated

A confused bank teller transposed the dollars and cents when he cashed a check for Mrs. Smith, giving her dollars instead of cents and cents instead of dollars.
After buying a newspaper for 50 cents , Mrs Smith noticed that she had exactly three times as much money as the original check. What was the original amount of the check?

Thanks so Much

 

[Denis]

A confused bank teller transposed the dollars and cents when he cashed a check for Mrs. Smith, giving her dollars instead of cents and cents instead of dollars.
After buying a newspaper for 50 cents , Mrs Smith noticed that she had exactly three times as much money as the original check. What was the original amount of the check?

x = dollars, y = cents
original check = 100x + y
reversed amount = 100y + x

Follow that? Example: $12.36; 12*100 + 36 = 1200 + 36 = 1236 ; ok?
Reversing it: 36*100 + 12 = 3600 + 12 = 3612 ; ok?
So we're dealing with cents only; $12.36 = 1236 cents.

equation (reversed - 50 cents = 3 times original):
100y + x - 50 = 3(100x + y)
100y + x - 50 = 300x + 3y
97y = 299x + 50
y = (299x + 50) / 97

That's as far as you can go.
You now need to find an x so that (299x + 50) is divisible by 97.
Start with x=1, and keep going until you hit paydirt...and that's x=18.

I think you can finish it now...