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Niall owes [tex]\$187[/tex] to his cousin. He hopes to earn money by painting a house, where he gets paid every 2 hours he paints.

Which equation 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 :

Niall owes \[tex]$187 initially. We are told that he is paid every 2 hours he paints and that his payment is \$[/tex]34 per 2 hours. This means his hourly wage is

[tex]$$
\frac{34}{2} = 17 \text{ dollars per hour}.
$$[/tex]

Letting [tex]$x$[/tex] be the number of hours he spends painting, his earnings from painting will be

[tex]$$
17x.
$$[/tex]

After paying back his cousin, his net money is calculated by subtracting his debt from his earnings. Therefore, the equation modeling the situation is:

[tex]$$
y = 17x - 187.
$$[/tex]

So, the correct answer is option D.

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