Final answer:
Daniel can work a combination of hours at two different restaurants to earn his goal of $105.30 a week. For example, he could work 10 hours at the first restaurant earning $5.35 per hour and approximately 8.29 hours at the second restaurant earning $6.25 per hour. There are many possible hour combinations that would allow him to meet his weekly earnings goal.
Step-by-step explanation:
To determine the number of hours Daniel could work at each restaurant to earn a total of $105.30 a week, we can set up a system of equations based on the wages he earns at each restaurant. Let's define x as the number of hours Daniel works at the restaurant where he earns $5.35 per hour, and y as the number of hours he works at the restaurant where he earns $6.25 per hour. The equation representing his total earnings would then be:
5.35x + 6.25y = 105.30
There are multiple combinations of x and y that can satisfy this equation, so let's look at a sample solution:
If Daniel decided to work 10 hours at the first restaurant: 5.35 * 10 = $53.50,
He would then need to earn: $105.30 - $53.50 = $51.80 at the second restaurant.
To find out how many hours he must work at the second restaurant to earn $51.80: $51.80 / 6.25 = approximately 8.29 hours.
So, one possible solution is that Daniel could work 10 hours at the first restaurant and about 8.29 hours at the second restaurant to earn $105.30 a week.
It is important to note that there are many possible combinations of hours that Daniel could work at both restaurants to reach his goal of $105.30. He could decide to work more hours at the restaurant with higher pay, or vice versa. As long as the total sum from both restaurants equals $105.30, the requirement will be satisfied.