Question

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There are three numbers for the combination to the bank's safe. The first number is 15. The other two numbers can be multiplied together to give a product of 24. What are the possibilities for the other two numbers? Write your answers as multiplication equations, and then write all of the possible combinations to the safe.

Answer 1

Let A and B represent the unknown numbers. The bank safe combination is of the form 15-A-B.

The variables A and B multiply to 24, so AB = 24 is the equation to set up.

Here's the entire set of possible A,B values dealing with positive integers only.

`\begin{array}c\cline{1-2}\text{A} & \text{B}\\ \cline{1-2}1 & 24\\ \cline{1-2}2 & 12\\ \cline{1-2}3 & 8\\ \cline{1-2}4 & 6\\ \cline{1-2}6 & 4\\ \cline{1-2}8 & 3\\ \cline{1-2}12 & 2\\ \cline{1-2}24 & 1\\ \cline{1-2}\end{array}`

Since a combination like 15-4-6 is different from 15-6-4, this means the solution (A,B) = (4,6) is different from (A,B) = (6,4). Overall, the order matters in this bank safe combination.