You earn $9.75 per hour at a part-time job. Your friend earns $9.35 per hour at a part-time job. The only other income you and your friend earn is a weekly allowance.
Determine whether it is possible for you and your friend to work the same number of hours and earn the same total amount in a given week for the following situations. Explain your reasoning
Your allowance is $20 per week, your friend’s allowance is $20 per week, and your friend receives a $0.40 raise.
To determine if it is possible for you and your friend to work the same number of hours and earn the same total amount in a given week, we need to compare the total earnings of each person in different scenarios.
Scenario 1:
You work x hours and earn 9.75x dollars.
Your friend works x hours and earns 9.35x dollars.
You both receive an allowance of 20 dollars each.
In this scenario, the total earnings for you would be 9.75x + 20 dollars, and for your friend would be 9.35x + 20 dollars.
Scenario 2:
Your friend receives a $0.40 raise, so their new rate is 9.35 + 0.40 = 9.75 dollars per hour.
You both work x hours and earn the same rate of 9.75 dollars per hour.
You both receive the same allowance of 20 dollars each.
In this scenario, the total earnings for you would be 9.75x + 20 dollars, and for your friend would be 9.75x + 20 dollars.
Comparing the total earnings in both scenarios, we see that the expressions for the total earnings are the same for both you and your friend. Therefore, in both scenarios, you and your friend will earn the same total amount in a given week if you work the same number of hours.
So, regardless of whether your friend receives a raise or not, it is possible for you and your friend to work the same number of hours and earn the same total amount in a given week.