Est. 1998 — 27 years of woodworking knowledge
Friday Puzzler -- Cashed Check
Alex Y
I had no cash with me when I went to the bank to cash a check. When he cashed the check, the teller made an error, switching the dollars and cents part of the payment. I.e., he gave me as many dollars as I should have gotten cents, and as many cents as I should have gotten dollars.
I didn't notice until I bought a pack of gum for $0.50, and saw that i then had left exactly twice as much money as the check was written for.
What was the amount of the check?
Re: Friday Puzzler -- Cashed Check
Larry Barrett
Nothing obvious (to me, at least) about this one. I had to write a little excel spreadsheet to get there.
I think the NCAA playoffs, coming up before long, enter the picture - I always like the Sweet Sixteens.
Sounds right
Alex Y
Nothing obvious or AHA! about this one. Was your spreadsheet a "brute force" approach? There is an analytic approach, but since you obfuscated the answer, I will leave it out there to see if anyone else wants to try (and check their answer against your hint).
Re: Sounds right
Larry Barrett
Brute force for awhile. Then saw that the value for the cents had to be close to twice the value of the dollars in the check. Then an equation and, with the help of Mr Excel, a solution.
Nice solution
Alex Y
Mine was more mechanical; less insightful.
Re: Nice solution
Larry Barrett
If the check is D+.01C, then the equation is (C+.01D-.5)=2(D+.01C).
Solve for C or D and use Excel to find a solution. There is only one, I think.
Re: Nice solution
Alex Y
That's the same approach I took, up until the Excel step
Restating as .98C - 1.99D = .5, you can see that C needs to be about twice as big as D
You can also see that every time you add 2 to C and 1 to D, you decrease the value on the left by 0.03.
Do that sixteen times as you get
.98*32 -1.99*16 = -0.48
Add one more to C, and you get .98-.48 = .50.