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Answer :
To solve this problem, we need to establish an equation based on the information given:
1. We have two positive integers whose product is 176.
2. One integer is 5 less than the other integer.
Let's call the greater integer [tex]\( x \)[/tex]. According to the problem, the other integer would then be [tex]\( x - 5 \)[/tex].
Since their product is 176, we can set up the equation:
[tex]\[
x \times (x - 5) = 176
\][/tex]
Now let's break down the options to find which one matches our equation:
- [tex]\( x^2 + 5 = 176 \)[/tex] is incorrect because it doesn't represent the product of two factors.
- [tex]\( x(x + 5) = 176 \)[/tex] is incorrect because it suggests one integer is 5 more than the other, which is not the case here.
- [tex]\( x(x - 5) = 176 \)[/tex] correctly represents our scenario: the product of two integers where one is 5 less than the other is 176.
- [tex]\( x^2 - 5 = 176 \)[/tex] is incorrect because it doesn't account for one integer being less than the other.
Hence, the correct equation to find the greater integer [tex]\( x \)[/tex] is:
[tex]\[
x(x - 5) = 176
\][/tex]
1. We have two positive integers whose product is 176.
2. One integer is 5 less than the other integer.
Let's call the greater integer [tex]\( x \)[/tex]. According to the problem, the other integer would then be [tex]\( x - 5 \)[/tex].
Since their product is 176, we can set up the equation:
[tex]\[
x \times (x - 5) = 176
\][/tex]
Now let's break down the options to find which one matches our equation:
- [tex]\( x^2 + 5 = 176 \)[/tex] is incorrect because it doesn't represent the product of two factors.
- [tex]\( x(x + 5) = 176 \)[/tex] is incorrect because it suggests one integer is 5 more than the other, which is not the case here.
- [tex]\( x(x - 5) = 176 \)[/tex] correctly represents our scenario: the product of two integers where one is 5 less than the other is 176.
- [tex]\( x^2 - 5 = 176 \)[/tex] is incorrect because it doesn't account for one integer being less than the other.
Hence, the correct equation to find the greater integer [tex]\( x \)[/tex] is:
[tex]\[
x(x - 5) = 176
\][/tex]
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