High School

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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 carefully consider the information given:

We have two positive integers whose product is 176. According to the problem, one integer is 5 less than the other. We need to find which equation represents this situation with [tex]\(x\)[/tex] as the greater integer.

1. Define the Variables:
- Let [tex]\(x\)[/tex] be the greater integer.
- The other integer, therefore, will be [tex]\(x - 5\)[/tex] because it's 5 less than the greater integer.

2. Translate to an Equation:
- According to the problem, the product of these two integers needs to equal 176. Thus, the equation based on the given conditions would be:
[tex]\[
x \cdot (x - 5) = 176
\][/tex]

So, the proper equation that models this particular situation is:
[tex]\[ x(x - 5) = 176 \][/tex]

This representation allows us to solve for [tex]\(x\)[/tex], the greater integer.

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Rewritten by : Barada