Question

anne and kyleigh worked over summer vacation.
the equation below represents the amount of money anne earned after x hours of work.
$y = \\$8.75x$
the table below shows the amount of money kyleigh earned after x hours of work.

hours	income
4	$57.00
8	$114.00
12	$171.00
16	$228.00

who earned more money per hour at their job?
a. kyleigh earned more money per hour.
b. anne and kyleigh earned the same amount of money per hour.
c. there is not enough information to determine their hourly wage.
d. anne earned more money per hour.

Explanation:

Step1: Find Anne's hourly wage

Anne's earnings are given by \( y = \$8.75x \). The coefficient of \( x \) is the hourly wage, so Anne earns \$8.75 per hour.

Step2: Find Kyleigh's hourly wage

Using the table, for 4 hours, income is \$57.00. Hourly wage = LXI0? Wait, no, wait, let's check again. Wait, no, wait, maybe I miscalculated. Wait, no, let's take another row. For 8 hours, income is \$114.00. So hourly wage is \( \frac{114.00}{8} = 14.25 \)? Wait, that can't be. Wait, no, wait, the user's original problem: Wait, no, wait, the equation for Anne is \( y = 8.75x \), so Anne's hourly wage is \$8.75. Wait, but Kyleigh's table: 4 hours, \$57. So \( 57 \div 4 = 14.25 \)? But that contradicts. Wait, no, maybe I made a mistake. Wait, no, wait, the problem's table: let's check 4 hours, \$57. So LXI4, 8 hours: 114 ÷ 8 = 14.25, 12 hours: 171 ÷ 12 = 14.25, 16 hours: 228 ÷ 16 = 14.25. Wait, but Anne's is 8.75. Wait, that can't be. Wait, no, wait, the user's question: Wait, maybe I misread the equation. Wait, the equation is LXI5? Wait, no, maybe it's a typo? Wait, no, the user's problem: Wait, no, let's recalculate Kyleigh's hourly wage. Wait, 57 divided by 4 is 14.25? But 14.25 times 4 is 57, 14.25 times 8 is 114, 14.25 times 12 is 171, 14.25 times 16 is 228. So Kyleigh's hourly wage is \$14.25, and Anne's is \$8.75? But that would mean Kyleigh earns more. But the original selected option was B. Wait, maybe I misread the equation. Wait, the equation is \( y = 8.75x \)? Wait, no, maybe it's \( y = 14.25x \)? Wait, no, the user's problem: Let me check again.

Wait, the user's problem: Anne's equation is \( y = \$8.75x \), so her hourly wage is \$8.75. Kyleigh's table: 4 hours, \$57. So \( 57 \div 4 = 14.25 \), 8 hours: 114 ÷ 8 = 14.25, 12 hours: 171 ÷ 12 = 14.25, 16 hours: 228 ÷ 16 = 14.25. So Kyleigh's hourly wage is \$14.25, which is more than Anne's \$8.75. So the correct answer should be A. Kyleigh earned more money per hour.

Wait, but the original selected option was B, which is wrong. So let's correct that.

Step1: Determine Anne's hourly rate

Anne's earnings are modeled by \( y = 8.75x \), where \( y \) is income and \( x \) is hours. The slope (coefficient of \( x \)) is the hourly wage, so Anne earns \$8.75 per hour.

Step2: Determine Kyleigh's hourly rate

Using the table, take the first row: 4 hours, \$57.00. Hourly wage = LXI0 dollars per hour. Let's verify with another row: 8 hours, \$114.00. \( \frac{114.00}{8} = 14.25 \) dollars per hour. So Kyleigh's hourly wage is \$14.25.

Step3: Compare the two hourly rates

Anne: \$8.75 per hour. Kyleigh: \$14.25 per hour. Since \( 14.25 > 8.75 \), Kyleigh earned more per hour.

Answer:

A. Kyleigh earned more money per hour.