Search

View Help

Applications using Factoring:
Set up an algebraic equation and then solve the following problems.
1. An integer is 3 less than 5 times another. If the product of the two integers is 36 , then find the integers.

Step 1 ：Let's denote the two integers as x and y.

Step 2 ：The first equation based on the problem is $y=5x-3$.

Step 3 ：The second equation based on the problem is $xy=36$.

Step 4 ：We can substitute y from the first equation into the second equation and solve for x.

Step 5 ：Then we can substitute x into the first equation to find y.

Step 6 ：The solutions for x and y are $(-12/5,-15)$ and $(3,12)$.

Step 7 ：However, the problem states that the integers are x and y. Therefore, we discard the solution $(-12/5,-15)$ because -12/5 is not an integer.

Step 8 ：The solution $(3,12)$ is the pair of integers that satisfy the conditions of the problem.

Step 9 ：Final Answer: The integers are $\boxed{{\displaystyle 3}}$ and $\boxed{{\displaystyle 12}}$.