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Answer :
Let's work through this problem step-by-step to find the correct equation.
1. Determine Niall's hourly rate of pay:
- Niall earns [tex]$34 for every 2 hours he works.
- To find out what he earns per hour, you divide the total pay for 2 hours by 2:
\[
\frac{\$[/tex]34}{2} = \[tex]$17 \text{ per hour}
\]
2. Set up the equation:
- Niall owes his cousin \$[/tex]187, so we need to subtract this amount from the money he earns to find out how much he will have left after paying back his cousin.
- Let [tex]\( x \)[/tex] represent the number of hours he spends painting.
- The amount of money Niall earns from painting for [tex]\( x \)[/tex] hours is [tex]\( 17x \)[/tex].
- After paying back his cousin, the amount he will have is modeled by the equation:
[tex]\[
y = 17x - 187
\][/tex]
So, the correct equation that models [tex]\( y \)[/tex], the amount of money he will have after paying back his cousin, in terms of [tex]\( x \)[/tex], the number of hours he spends painting, is:
D. [tex]\( y = 17x - 187 \)[/tex]
1. Determine Niall's hourly rate of pay:
- Niall earns [tex]$34 for every 2 hours he works.
- To find out what he earns per hour, you divide the total pay for 2 hours by 2:
\[
\frac{\$[/tex]34}{2} = \[tex]$17 \text{ per hour}
\]
2. Set up the equation:
- Niall owes his cousin \$[/tex]187, so we need to subtract this amount from the money he earns to find out how much he will have left after paying back his cousin.
- Let [tex]\( x \)[/tex] represent the number of hours he spends painting.
- The amount of money Niall earns from painting for [tex]\( x \)[/tex] hours is [tex]\( 17x \)[/tex].
- After paying back his cousin, the amount he will have is modeled by the equation:
[tex]\[
y = 17x - 187
\][/tex]
So, the correct equation that models [tex]\( y \)[/tex], the amount of money he will have after paying back his cousin, in terms of [tex]\( x \)[/tex], the number of hours he spends painting, is:
D. [tex]\( y = 17x - 187 \)[/tex]
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