Question

My young cousins worked part-time jobs over the summer to save money for a car. The job paid
different rates for working weekdays and weekends. During the first week, one cousin worked 22 hours
during the week and one hour on the weekend, earning $232. Her sister earned $270 by working 15
hours during the week and 10,hours on the weekend. What was the hourly pay rate for working
weekdays and weekends?

Answer 1

Answer:

W) is $10, and the hourly pay rate for working on weekends (

�

E) is $12.

Step-by-step explanation:

Let's denote the hourly pay rate for working on weekdays as

�

W and the hourly pay rate for working on weekends as

�

E.

For the first cousin, who worked 22 hours during the week (

�

W) and 1 hour on the weekend (

�

E), earning $232:

22

�

+

1

�

=

232

22W+1E=232

For the second cousin, who worked 15 hours during the week (

�

W) and 10 hours on the weekend (

�

E), earning $270:

15

�

+

10

�

=

270

15W+10E=270

Now, we have a system of two equations with two unknowns:

{

22

�

+

�

=

232

15

�

+

10

�

=

270

{

22W+E=232

15W+10E=270

​

Let's solve this system to find the values of

�

W and

�

E.

Multiply the first equation by 10 to eliminate

�

E:

{

220

�

+

10

�

=

2320

15

�

+

10

�

=

270

{

220W+10E=2320

15W+10E=270

​

Now, subtract the second equation from the first:

205

�

=

2050

205W=2050

Divide both sides by 205:

�

=

10

W=10

Now that we know

�

W, substitute it back into one of the original equations. Let's use the first one:

22

(

10

)

+

�

=

232

22(10)+E=232

220

+

�

=

232

220+E=232

�

=

12

E=12

So, the hourly pay rate for working on weekdays (

�

W) is $10, and the hourly pay rate for working on weekends (

�

E) is $12.