Mathematical & Logic Question?

Question

When john cashed his cheque, the bank teller gave him dollars instead of cents, and cents instead of dollars. After he gave five cents to a begger, he found that he had left exactly twice as much as his original cheque. What was the amount of the cheque?

Can you please show me how to calculate the amount of the cheque? Thanks

Answer 1

Let C be the number of cents and D be the number of dollars -- then we can set up this relationship:

100C+D-5 = 2*(100D+C)

The left had side gives us 100* the number of cents plus the number of dollars (think of this as the number of pennies he got when he cashed the check) minus the five cents he gave to the begger.

He was supposed to get 100D+C -- so the right hand side is twice that.

From this, we get the following relationships:

98C=199D+5

C = (199D+5)/98

This looks like there should be many solutions to the problem. But we hav esome other information. C has to be a whole number -- which mens that (199D+5) has to be a multiple of 98. We also know that the number of cents has to be between zero and 99.

The only solution is D = 31 and C = 63 -- so the check was for $31.63