Question

eva is starting a new job. she earns an hourly wage, and the cost of her uniform is taken out of her first paycheck. she makes a table showing different numbers of hours she could work, x, and the amount that her first paycheck would be, y.

evas paycheck

number of hours worked, x	first paycheck amount, y (dollars)
5	46.25
7	74.75
9	103.25
12	146.00

based on the table, what is evas hourly wage and what is the cost of her uniform?

move the correct answer to each box. not all answers will be used.

$2.00 $3.50 $9.25 $12.00 $14.25 $25.00

hourly wage: \boxed{} per hour

uniform cost: \boxed{}

Explanation:

Step1: Find the hourly wage

Let the hourly wage be \( m \) and the uniform cost be \( b \). The equation is \( y = mx - b \) (since uniform cost is deducted). Take two points, say \( (2, 3.50) \) and \( (5, 46.25) \). The slope \( m \) (hourly wage) is \( \frac{46.25 - 3.50}{5 - 2}=\frac{42.75}{3}=14.25 \)? Wait, no, wait, maybe I mixed up. Wait, when \( x = 2 \), \( y = 3.50 \)? Wait, that can't be. Wait, maybe the first entry is a typo? Wait, no, maybe I misread. Wait, looking again: when \( x = 2 \), \( y = 3.50 \)? But when \( x = 5 \), \( y = 46.25 \). Wait, no, maybe the first value is \( 3.50 \) is wrong? Wait, no, maybe I miscalculated. Wait, let's take \( x = 5 \) and \( x = 7 \). \( 74.75 - 46.25 = 28.5 \), \( 7 - 5 = 2 \), so \( 28.5 / 2 = 14.25 \). Wait, \( x = 9 \): \( 103.25 - 74.75 = 28.5 \), \( 9 - 7 = 2 \), so \( 28.5 / 2 = 14.25 \). \( x = 12 \): \( 146 - 103.25 = 42.75 \), \( 12 - 9 = 3 \), \( 42.75 / 3 = 14.25 \). Ah, so the hourly wage \( m = 14.25 \)? Wait, but when \( x = 2 \), \( y = 3.50 \). Let's check the uniform cost \( b \). Using \( y = mx - b \), so \( b = mx - y \). For \( x = 5 \), \( m = 14.25 \), \( y = 46.25 \). So \( b = 14.25 * 5 - 46.25 = 71.25 - 46.25 = 25 \). Let's check with \( x = 2 \): \( 14.25 * 2 - 25 = 28.5 - 25 = 3.50 \), which matches. So hourly wage is \( 14.25 \), uniform cost is \( 25 \). Wait, but the options include \( \$14.25 \) and \( \$25.00 \). So that makes sense.

Step2: Confirm uniform cost

Using the equation \( y = 14.25x - b \). For \( x = 5 \), \( 46.25 = 14.25*5 - b \). \( 14.25*5 = 71.25 \), so \( b = 71.25 - 46.25 = 25 \). Which is one of the options. And hourly wage is \( 14.25 \).

Answer:

Hourly wage: $\$14.25$ per hour
Uniform cost: $\$25.00$