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 $10 per week and your friend’s allowance is $20 per week.
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 both scenarios.
Let's assume you work for x hours in a week. Your total earnings would be:
Total earnings = (hourly wage) x (number of hours) + (allowance)
Total earnings = $9.75x + $10
Similarly, let's assume your friend works for x hours in a week. Your friend's total earnings would be:
Total earnings = (hourly wage) x (number of hours) + (allowance)
Total earnings = $9.35x + $20
For you and your friend to earn the same total amount, we need to equate the two total earnings equations:
$9.75x + $10 = $9.35x + $20
Subtracting $9.35x from both sides:
$0.40x + $10 = $20
Subtracting $10 from both sides:
$0.40x = $10
Dividing both sides by $0.40 to solve for x:
x = $10 / $0.40
x = 25
Therefore, for you and your friend to work the same number of hours and earn the same total amount in a given week, you would both need to work 25 hours.