Let's solve this step-by-step:
1. Let's denote Caitlyn's age as [tex]\( x \)[/tex].
2. Carl is two years older than Caitlyn, so Carl's age can be represented as [tex]\( x + 2 \)[/tex].
3. Daryl is five years older than Carl, so Daryl's age can be represented as [tex]\( (x + 2) + 5 \)[/tex], which simplifies to [tex]\( x + 7 \)[/tex].
4. Now, the given problem states that the product of Carl's and Daryl's ages is at least 160. Thus the inequality can be written as:
[tex]\[ (x + 2)(x + 7) \geq 160 \][/tex]
Let's expand the product to better understand the inequality:
[tex]\[ (x + 2)(x + 7) = x^2 + 7x + 2x + 14 = x^2 + 9x + 14 \][/tex]
So the inequality representing the situation is:
[tex]\[ x^2 + 9x + 14 \geq 160 \][/tex]
The correct answer is:
[tex]\[ x^2 + 9x + 14 \geq 160 \][/tex]
