A cashier mentally reversed the digits of one customer's

BTGmoderatorLU wrote:A cashier mentally reversed the digits of one customer's correct amount of changed and thus gave the customer an incorrect amount of change. If the cash register contained 45 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?

A. 14
B. 45
C. 54
D. 65
E. 83

We can PLUG IN THE ANSWERS, which represent the correct amount of change.
When the digits in the correct answer are reversed, the resulting integer must yield a decrease of 45 cents -- the 45 cents left in the register by mistake.

Since reversing the digits must yield a decrease of 45 cents, the correct answer must be greater than 45.
Eliminate A and B.

C: 54-45 = 9
D: 65-56 = 9
E: 83-38 = 45.

Only the option in blue yields a decrease of 45 cents.

The correct answer is E.

BTGmoderatorLU wrote:A cashier mentally reversed the digits of one customer's correct amount of changed and thus gave the customer an incorrect amount of change. If the cash register contained 45 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?

A. 14
B. 45
C. 54
D. 65
E. 83

The correct amount of change must have the tens digit greater than the units digit so that when the digits are reversed, the tens digit will be less than the units digit, and hence, the cash register could have contained 45 cents more than it should have.

Let’s check choice E first.

If the correct change is 83 cents, the incorrect change is 38 cents and the difference is 83 - 38 = 45 cents. This fits the information given in the problem. Thus, 83 cents must be the correct change.

Alternate Solution:

Let’s let the correct amount of change be ab, where a is the tens digit and b is the units digit. We can express the value of this number as 10a + b.

The reversed number is ba, where b is now the tens digit and a is now the units digit. We can express the value of this number as 10b + a.

We know that the difference between the correct change and its reversed value is 45 cents. Thus, we have:

(10a + b) – (10b + a) = 45

10a + b – 10b – a = 45

9a – 9b = 45

9(a – b) = 45

a – b = 5

We see that the difference of the two digits is 5. The only answer choice that fits this criterion is choice E: 83.

Answer: E