College

Select the correct answer.

Niall owes [tex]\$187[/tex] to his cousin. He hopes to earn some money by painting a house. He gets paid [tex]\$34[/tex] for 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 :

We are given that Niall owes \[tex]$187 to his cousin, so his starting balance is:

$[/tex][tex]$-187.$[/tex][tex]$

He earns \$[/tex]34 for every 2 hours of painting. Thus, his hourly rate is:

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

Since he earns money at a constant rate (a linear relationship), we can model the total amount of money he has (after paying back his cousin) with the linear equation in slope-intercept form:

[tex]$$y = mx + b,$$[/tex]

where
- [tex]$m$[/tex] is the hourly rate (slope), and
- [tex]$b$[/tex] is the starting balance (y-intercept).

Substituting the values we have:

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

Thus, the equation that models his total amount of money after painting for [tex]$x$[/tex] hours is:

[tex]$$\boxed{y = 17x - 187}.$$[/tex]

This corresponds to option D.