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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, we need to find two positive integers whose product is 176, and one of the integers is 5 less than the other.

Let's call the greater integer [tex]\( x \)[/tex]. The smaller integer will then be [tex]\( x - 5 \)[/tex] because it is 5 less than the greater integer.

To set up the equation, we use the fact that the product of these two integers is 176:

[tex]\[ x(x - 5) = 176 \][/tex]

This equation accurately represents the problem because it encapsulates the relationship between the two integers, where one is 5 less than the other, and their product is 176.

Therefore, the correct equation to find the value of [tex]\( x \)[/tex], the greater integer, is:

[tex]\[ x(x - 5) = 176 \][/tex]

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