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Answer :
Let's work through the problem together step by step to find the equation that models the amount of money Niall will have after paying back his cousin.
1. Understanding the Problem:
- Niall owes [tex]$187 to his cousin.
- He earns $[/tex]34 for every 2 hours he paints.
- We need to find the equation that represents the money he will have after paying back [tex]$187.
2. Calculate the Hourly Rate:
- Since Niall earns $[/tex]34 for 2 hours of work, we need to find out how much he earns per hour.
- To find the hourly rate, divide [tex]$34 by 2:
\( \text{Hourly rate} = \frac{34}{2} = 17 \) dollars per hour.
3. Formulate the Equation:
- Let \( x \) be the number of hours Niall spends painting.
- The amount of money Niall earns after \( x \) hours is \( 17x \) dollars, because he earns $[/tex]17 per hour.
- Before counting the money he'll have after painting, we need to subtract the amount he owes to his cousin, which is $187.
- The equation to represent how much money he will have after paying back his cousin is:
[tex]\( y = 17x - 187 \)[/tex].
4. Select the Correct Answer:
- Now, looking at the provided options, the equation that matches is:
- D. [tex]\( y = 17x - 187 \)[/tex]
Therefore, the correct answer is D. [tex]\( y = 17x - 187 \)[/tex].
1. Understanding the Problem:
- Niall owes [tex]$187 to his cousin.
- He earns $[/tex]34 for every 2 hours he paints.
- We need to find the equation that represents the money he will have after paying back [tex]$187.
2. Calculate the Hourly Rate:
- Since Niall earns $[/tex]34 for 2 hours of work, we need to find out how much he earns per hour.
- To find the hourly rate, divide [tex]$34 by 2:
\( \text{Hourly rate} = \frac{34}{2} = 17 \) dollars per hour.
3. Formulate the Equation:
- Let \( x \) be the number of hours Niall spends painting.
- The amount of money Niall earns after \( x \) hours is \( 17x \) dollars, because he earns $[/tex]17 per hour.
- Before counting the money he'll have after painting, we need to subtract the amount he owes to his cousin, which is $187.
- The equation to represent how much money he will have after paying back his cousin is:
[tex]\( y = 17x - 187 \)[/tex].
4. Select the Correct Answer:
- Now, looking at the provided options, the equation that matches is:
- D. [tex]\( y = 17x - 187 \)[/tex]
Therefore, the correct answer is D. [tex]\( y = 17x - 187 \)[/tex].
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