Answer :
To solve this problem, let's first understand the key pieces of information given:
1. Niall's Debt: Niall owes [tex]$187 to his cousin.
2. Earning Rate: Niall gets paid $[/tex]34 for every 2 hours he paints.
We need to find an 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.
Here's the step-by-step process:
### Step 1: Determine the hourly pay rate
Niall gets paid \[tex]$34 for every 2 hours. To find out how much he earns per hour:
\[
\text{Pay rate per hour} = \frac{34}{2} = 17 \text{ dollars per hour}
\]
### Step 2: Establish the earnings equation
If \( x \) is the number of hours he spends painting, his total earnings from painting would be:
\[
\text{Total earnings} = 17x \text{ dollars}
\]
### Step 3: Calculate money after paying back the debt
Niall owes \$[/tex]187 to his cousin. Therefore, the money he will have after paying back his cousin can be modeled as:
[tex]\[
y = 17x - 187
\][/tex]
### Step 4: Identify the correct equation from the options
Based on our calculations, the equation that models the amount of money [tex]\( y \)[/tex] he will have after paying his cousin, in terms of [tex]\( x \)[/tex] hours of painting, is:
[tex]\[
y = 17x - 187
\][/tex]
### Conclusion
The correct answer is:
[tex]\[
\boxed{D.\ y = 17x - 187}
\][/tex]
1. Niall's Debt: Niall owes [tex]$187 to his cousin.
2. Earning Rate: Niall gets paid $[/tex]34 for every 2 hours he paints.
We need to find an 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.
Here's the step-by-step process:
### Step 1: Determine the hourly pay rate
Niall gets paid \[tex]$34 for every 2 hours. To find out how much he earns per hour:
\[
\text{Pay rate per hour} = \frac{34}{2} = 17 \text{ dollars per hour}
\]
### Step 2: Establish the earnings equation
If \( x \) is the number of hours he spends painting, his total earnings from painting would be:
\[
\text{Total earnings} = 17x \text{ dollars}
\]
### Step 3: Calculate money after paying back the debt
Niall owes \$[/tex]187 to his cousin. Therefore, the money he will have after paying back his cousin can be modeled as:
[tex]\[
y = 17x - 187
\][/tex]
### Step 4: Identify the correct equation from the options
Based on our calculations, the equation that models the amount of money [tex]\( y \)[/tex] he will have after paying his cousin, in terms of [tex]\( x \)[/tex] hours of painting, is:
[tex]\[
y = 17x - 187
\][/tex]
### Conclusion
The correct answer is:
[tex]\[
\boxed{D.\ y = 17x - 187}
\][/tex]
