High School

Select the correct answer.

Niall owes [tex] \$187 [/tex] to his cousin. However, he doesn't have any money right now. He hopes to earn some money by painting a house. He gets paid [tex] \$34 [/tex] for every 2 hours he paints. Which equation of a line 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?

A. [tex] y = 34x - 187 [/tex]
B. [tex] y = 17x + 187 [/tex]
C. [tex] y = 34x + 187 [/tex]
D. [tex] y = 17x - 187 [/tex]

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.