Carissa works as a babysitter during her summer vacation. she gets paid one rate for daytime hours and a higher rate for nighttime hours. one week, she worked 12 daytime hours and 4 nighttime hours and earned $120. the next week, she earned $60 for a total of 4 daytime hours and 3 nighttime hours. let x represent the hourly daytime rate and y represent her hourly nighttime rate.

The hourly daytime rate is 6 and the hourly nighttime rate is 12 and this can be determined by forming the linear equation.

Given :

The linear equation can be formed in order to determine the hourly daytime rate and the hourly nighttime rate.

So, the linear equation that represents the first week earning is:

12x + 4y = 120

3x + y = 30

y = 30 - 3x    --- (1)

The linear equation that represents the second-week earning is:

4x + 3y = 60   --- (2)

Substitute the value of 'y' in equation (2).

4x + 3(30 - 3x) = 60

4x + 90 - 9x = 60

5x = 30

x = 6

Substitute the value of 'x' in equation (1).

y = 30 - 3(6)

y = 30 - 18

y = 12

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