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Teller (Posted on 2024-02-11)

Mr. Zngg cashed a check for D dollars and C cents at the Bank of Dinkydonk. The teller accidentally reversed the figures and gave him C dollars and D cents. Suppose he got more than N times the original amount, but not more than N+1 times.

(1) For what check value can Mr. Zngg spend the least money and end up with exactly N times the original amount?

(2) For what check value must Mr. Zngg spend the most money in order to end up with exactly N times the original amount?

(3) For what check value can Mr. Zngg spend an amount of money closest to his original check and end up with exactly N times the right amount? [The amount of the check will determine the value of N, which must be a positive integer. D and C are both 2-digit numbers.]

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

(1): If the original check was $12.37, he received $37.12 which is 3.0008084074373484 the amount of the check.
If he were to spend 1 penny, the ratio would be 37.11 / 12.37 = 3 = N
(2): If the original check was for $49.99, he received $99.49 which is 1.9901980396079213 the amount of the check.
If he were to spend $49.50, the ratio would be 49.99 / 49.99 = 1 = N
(3): If the original check was for $33.67, he received $67.33 which is 1.9997029997029998 the amount of the check.
If he were to spend $33.66, the ratio would be 33.67 / 33.67 = 1 = N
For an explanation, refer to the solution submitted by Larry in this location.

Comments: ( You must be logged in to post comments.)

	Subject	Author	Date
	Computer solution	Larry	2024-02-11 14:38:37

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