Stephen went to the bank to cash a check. By mistake, the teller gave him dollars instead of cents and cents instead of dollars, which he didn't notice. On the way out, Stephen spent a nickel at a gum machine. When Stephen returned home, he found he had exactly twice the amount of the check.

Determine the exact amount of the check Stephen cashed at the bank.

If the check is for 100d + c cents
and he got instead 100c + d cents

then according to the problem 2(100d + c) = 100c + d - 5
or d = (98c-5)/199
what is sought is a solution to this where c and d are both whole numbers less than 100.  It's easily solved with a table but even without on it's simple.
98*2 = 196 which is three short of 199 which means every 2 c will bring 98c - 5 closer to a multiple of 199 by 3.

When c = 1, 98c-5=93 which is 93 too high
When c = 3, 98c-5=289 which is 90 too high
93* 2/3 = 62 so maybe c=62
nope off by one
c = 63 gives d = 31

So the check was for $31.63 but the teller gave $63.31

Posted by Jer on 2012-12-19 14:04:32