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.

Question

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.

12 x + 4 y = 120. 4 x + 3 y = 60.

What is the solution to the system of equations?
(3,4)
(4, 12)
(6, 12)
(10, 30)

Answer 1

To solve the system of equations, we can use the method of substitution.

First, isolate one of the variables in one of the equations. Let's solve the second equation for x:

4x + 3y = 60
4x = 60 - 3y
x = (60 - 3y)/4

Now we can substitute this expression for x into the first equation:

12x + 4y = 120
12((60 - 3y)/4) + 4y = 120
3(60 - 3y) + 4y = 120
180 - 9y + 4y = 120
-5y = -60
y = 12

Now substitute this value of y into the expression for x:

x = (60 - 3(12))/4
x = (60 - 36)/4
x = 6

So the solution to the system of equations is (6, 12). The correct option is (6, 12).