College algebra

Question

an integer is 18 more than 4 times another. If the product of the two integers is 90, find the integers

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is to use the information given in order to set up an algebraic expression. On this one we have

x = 4y + 18   because an integer is 18 more than 4 times another

xy = 90     because the product of two integers is 90

from there then you want to solve for the values directly! I would plug in the first equation into the second

(4y + 18)y = 90

4y^2 + 18y = 90

4y^2 + 18y – 90 = 0

When I solve that using the quadratic formula I get y = 3, meaning x = 4(3) + 18 = 12 + 18 = 30

So the two integers that it’s after here are 30 and 3.

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

n = one of the integers

4n + 18 = the other integer

n(4n + 18) = 90

4n² + 18n - 90 = 0

n = 3 (there is another solution, but it is not an integer)

4n + 18 = 4(3) + 18 = 30