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Answer :
Sure! Let's work through the problem step by step to find the correct equation.
1. Understand the Problem:
- Niall owes [tex]$187 to his cousin.
- He gets paid $[/tex]34 for every 2 hours he paints.
2. Calculate His Earnings Per Hour:
- Niall earns [tex]$34 for 2 hours, which means his earnings per hour are:
\[
\frac{34}{2} = 17 \text{ dollars per hour}
\]
3. Write the Function for Earnings:
- Niall's earnings after \( x \) hours of painting would be \( 17x \) dollars.
4. Consider the Debt:
- Since he owes $[/tex]187, we need to subtract this amount from his total earnings to find out how much he has after paying back his cousin.
5. Formulate the Equation:
- Therefore, the amount of money he will have after paying back his cousin can be expressed as:
[tex]\[
y = 17x - 187
\][/tex]
The equation 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 option D.
1. Understand the Problem:
- Niall owes [tex]$187 to his cousin.
- He gets paid $[/tex]34 for every 2 hours he paints.
2. Calculate His Earnings Per Hour:
- Niall earns [tex]$34 for 2 hours, which means his earnings per hour are:
\[
\frac{34}{2} = 17 \text{ dollars per hour}
\]
3. Write the Function for Earnings:
- Niall's earnings after \( x \) hours of painting would be \( 17x \) dollars.
4. Consider the Debt:
- Since he owes $[/tex]187, we need to subtract this amount from his total earnings to find out how much he has after paying back his cousin.
5. Formulate the Equation:
- Therefore, the amount of money he will have after paying back his cousin can be expressed as:
[tex]\[
y = 17x - 187
\][/tex]
The equation 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 option D.
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