Sabrina has two part-time jobs delivering flyers. She earns $9/hour at her weekday job and $12/hour at her weekend job. Last week she worked 23 hours and earned a total of $231. Determine how many hours she worked at each job.
To determine the number of hours Sabrina worked at each job, we can set up a system of equations based on the information given.
Let's use the following variables:
x = number of weekday hours
y = number of weekend hours
From the given information, we can set up two equations:
Equation 1: Sabrina worked a total of 23 hours.
x + y = 23
Equation 2: Sabrina earned a total of $231.
9x + 12y = 231
To solve this system of equations, we can use substitution or elimination.
Let's solve using substitution:
1. Solve Equation 1 for x:
x = 23 - y
2. Substitute x in Equation 2 with its value from step 1:
9(23 - y) + 12y = 231
3. Distribute and simplify:
207 - 9y + 12y = 231
3y = 24
y = 8
4. Substitute y = 8 into Equation 1 to find x:
x + 8 = 23
x = 23 - 8
x = 15
Therefore, Sabrina worked 15 hours at her weekday job and 8 hours at her weekend job.
d + e = 23 ... 9 d + 9 e = 207
9 d +12 e = 231
subtracting equations (to eliminate d) ... 3 e = 24
solve for e , then substitute back to find d