Two positive integers have a product of 176. One integer is 5 less than the other integer. Which equation can be used to find the value of [tex]x[/tex], the greater integer?

A. [tex]x^2 + 5 = 176[/tex]
B. [tex]x(x + 5) = 176[/tex]
C. [tex]x(x - 5) = 176[/tex]
D. [tex]x^2 - 5 = 176[/tex]

Answer :

To solve this problem, let's break it down step-by-step:

1. Understand the problem:
We have two positive integers with a product of 176, and one integer is 5 less than the other. Our task is to find an equation that helps determine the greater integer, [tex]\( x \)[/tex].

2. Define variables:
- Let [tex]\( x \)[/tex] be the greater integer.
- Therefore, the other integer, being 5 less, is [tex]\( x - 5 \)[/tex].

3. Form an equation from the given conditions:
- We know the product of these two integers is 176. So, we can write the equation:
[tex]\[
x \times (x - 5) = 176
\][/tex]

4. Simplify and verify the equation:
- The equation [tex]\( x(x - 5) = 176 \)[/tex] directly represents the relationship stated in the problem where [tex]\( x \)[/tex] is multiplied by [tex]\( (x - 5) \)[/tex], giving the product 176.

Thus, the correct equation to use is:
[tex]\[
x(x - 5) = 176
\][/tex]
This equation is formed based on the given relationships and conditions in the problem statement.