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 and your friend’s allowance is $10 per week.
In order to determine if it is possible for both 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 from work and allowances for both situations.
For you:
Hourly wage = $9.75
Weekly allowance = $20
For your friend:
Hourly wage = $9.35
Weekly allowance = $10
Let's assume both you and your friend work "x" hours in a given week.
Your total earnings would be: 9.75x + 20
Your friend's total earnings would be: 9.35x + 10
For you and your friend to earn the same total amount, the following equation needs to be true:
9.75x + 20 = 9.35x + 10
Let's solve this equation:
9.75x - 9.35x = 10 - 20
0.4x = -10
x = -10/0.4
x = -25
The solution to this equation is a negative value, which means it is not possible to work a negative number of hours. Therefore, it is not 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 given situations.