Answer :
To solve this problem, we need to figure out how much money Niall will have after paying back his cousin, depending on the number of hours [tex]\( x \)[/tex] he spends painting. Let's break it down step by step:
1. Determine Hourly Earnings:
- Niall is paid [tex]$34 for every 2 hours he paints. To find out how much he earns per hour, we divide $[/tex]34 by 2:
[tex]\[
\text{Hourly rate} = \frac{34}{2} = 17
\][/tex]
- So, Niall earns [tex]$17 per hour.
2. Set Up the Equation:
- The amount Niall earns after painting for \( x \) hours would be \( 17x \), since he earns $[/tex]17 for each hour of painting.
- Niall owes $187, so if we subtract this debt from his earnings, the remaining amount he will have is represented by the equation:
[tex]\[
y = 17x - 187
\][/tex]
- Here, [tex]\( y \)[/tex] is the amount of money he will have after paying back his cousin.
3. Identify the Correct Option:
- The equation we have derived matches the option:
[tex]\[
\text{D. } y = 17x - 187
\][/tex]
Therefore, the correct answer is D: [tex]\( y = 17x - 187 \)[/tex].
1. Determine Hourly Earnings:
- Niall is paid [tex]$34 for every 2 hours he paints. To find out how much he earns per hour, we divide $[/tex]34 by 2:
[tex]\[
\text{Hourly rate} = \frac{34}{2} = 17
\][/tex]
- So, Niall earns [tex]$17 per hour.
2. Set Up the Equation:
- The amount Niall earns after painting for \( x \) hours would be \( 17x \), since he earns $[/tex]17 for each hour of painting.
- Niall owes $187, so if we subtract this debt from his earnings, the remaining amount he will have is represented by the equation:
[tex]\[
y = 17x - 187
\][/tex]
- Here, [tex]\( y \)[/tex] is the amount of money he will have after paying back his cousin.
3. Identify the Correct Option:
- The equation we have derived matches the option:
[tex]\[
\text{D. } y = 17x - 187
\][/tex]
Therefore, the correct answer is D: [tex]\( y = 17x - 187 \)[/tex].
