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Answer :
Sure, let's work through the problem step-by-step:
1. Niall owes [tex]$187 to his cousin.
2. He earns $[/tex]34 for every 2 hours of painting.
We need to express the amount of money Niall will have after paying back his cousin in terms of [tex]\( x \)[/tex], the number of hours he spends painting.
First, let's determine how much Niall earns per hour:
[tex]\[ \text{Earnings per 2 hours} = \$34 \][/tex]
[tex]\[ \text{Earnings per 1 hour} = \frac{34}{2} = \$17 \][/tex]
So, for [tex]\( x \)[/tex] hours of painting, Niall earns:
[tex]\[ 17x \][/tex]
Next, we need to consider the debt which is [tex]$\$[/tex]187$. After working [tex]\( x \)[/tex] hours and earning [tex]\( 17x \)[/tex] dollars, Niall will have to pay back the money he owes. The remaining amount of money he will have after paying off his debt is:
[tex]\[ \text{Remaining amount} = 17x - 187 \][/tex]
Therefore, the correct equation of a line that models [tex]\( y \)[/tex], the amount of money Niall will have after paying back his cousin, in terms of [tex]\( x \)[/tex], the number of hours he spends painting, is:
[tex]\[ y = 17x - 187 \][/tex]
So, the correct answer is:
D. [tex]\( y = 17x - 187 \)[/tex]
1. Niall owes [tex]$187 to his cousin.
2. He earns $[/tex]34 for every 2 hours of painting.
We need to express the amount of money Niall will have after paying back his cousin in terms of [tex]\( x \)[/tex], the number of hours he spends painting.
First, let's determine how much Niall earns per hour:
[tex]\[ \text{Earnings per 2 hours} = \$34 \][/tex]
[tex]\[ \text{Earnings per 1 hour} = \frac{34}{2} = \$17 \][/tex]
So, for [tex]\( x \)[/tex] hours of painting, Niall earns:
[tex]\[ 17x \][/tex]
Next, we need to consider the debt which is [tex]$\$[/tex]187$. After working [tex]\( x \)[/tex] hours and earning [tex]\( 17x \)[/tex] dollars, Niall will have to pay back the money he owes. The remaining amount of money he will have after paying off his debt is:
[tex]\[ \text{Remaining amount} = 17x - 187 \][/tex]
Therefore, the correct equation of a line that models [tex]\( y \)[/tex], the amount of money Niall will have after paying back his cousin, in terms of [tex]\( x \)[/tex], the number of hours he spends painting, is:
[tex]\[ y = 17x - 187 \][/tex]
So, the correct answer is:
D. [tex]\( y = 17x - 187 \)[/tex]
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