A woman went into a bank to cash an insurance refund check. By mistake the teller gave her dollars for cents and cents for dollars. She put the money in her purse but accidentally dropped a nickel on the floor. When she got home, she found that she had exactly twice the amount of the check she had cashed. She didn’t have any money in her wallet before going to the bank. What was the exact amount of that check?
Answer
The amount must have been $31.63. She received $63.31. After she dropped a nickel there would remain the sum of $63.26, which is twice the amount of the check.
If x is the dollar amount written on the check and y is the cents amount.
The original check amount was:
x+yThe amount that teller handed the lady was:100y+x/100The amount the lady found in her bag was:100y + x/100 - 0.05We know the lady found twice the amount of the original check:
2(x+y) = 100y + x/100 - 0.05They want you to solve for the original check amount
x+y.I messed up my algebra somewhere because I got:
x=(5+9800y)/199which if you set y = 0.63 you get x = 31.05 so I’m off somewhere.I wasn’t too far off, I dropped a minus sign somewhere.
I can’t think of a mathematical way to constrain x to be positive integers and constrain y to be any integer 0 to 99 divided by 100. Using a graph was a good idea