Faith is working two summer jobs, making $13 per hour lifeguarding and $12 per hour washing cars. Last week Faith worked a total of 10 hours and earned a total of $124. Write a system of equations that could be used to determine the number of hours Faith worked lifeguarding last week and the number of hours she worked washing cars last week. Define the variables that you use to write the system

The equation to determine the number of hours Faith worked lifeguarding last week and the number of hours she worked washing cars last week is

[tex]x + y = 10 [/tex]

[tex]13x + 12y = 124 [/tex]

Given:

Earning per hour lifeguarding = $13

Earning per hour washing cars = $12

Total hours worked = 10 hours

Total amount earned = $124

let

x = number of hours lifeguarding

y = number of hours car washing

The equation:

x + y = 10 (1)

x + y = 10 (1)13x + 12y = 124 (2)

multiply (1) by 12 to eliminate y

12x + 12y = 120 (3)

13x + 12y = 124 (2)

subtract (3) from (2)

x = 4 hours

substitute x = 4 into (1)

x + y = 10

4 + y = 10

y = 10 - 4

y = 6 hours

Therefore, number of hours Faith worked lifeguarding last week and the number of hours she worked washing cars last week is 4 hours and 6 hours respectively.