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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.

Respuesta :

texaschic101
x = daytime, y = nighttime

12x + 4y = 120
4x + 3y = 60...multiply by -3
-----------------
12x + 4y = 120
-12x - 9y = - 180 (result of multiplying by -3)
-----------------add
-5y = -60
y = -60/-5
y = 12 <== nighttime rate per hr

4x + 3y = 60
4x + 3(12) = 60
4x + 36 = 60
4x = 60 - 36
4x = 24
x = 24/4
x = 6 <== daytime rate per hr

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

Given :

  • 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.

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

For more information, refer to the link given below:

https://brainly.com/question/11897796

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