Jordan has two jobs, working at a local grocery store and tutoring at his school. Jordan earns $\$ 11$ an hour working at the grocery store and $\$ 22$ an hour while tutoring. On a given week Jordan must work no more than 40 total hours but must earn no less than 450 total dollars. If Jordan works 10 hours at the grocery store, what is an appropriate number of hours spent working at the tutoring center? hours Preview

Step 1 ：Jordan earns $11 per hour at the grocery store and $22 per hour at the tutoring center. He has already worked 10 hours at the grocery store, so he has earned \(11 \times 10 = 110\) dollars at the grocery store.

Step 2 ：He needs to earn at least $450 in total, so he still needs to earn \(450 - 110 = 340\) dollars.

Step 3 ：Since he earns $22 per hour at the tutoring center, he needs to work \(340 \div 22 = 15.45\) hours at the tutoring center. However, since he can't work a fraction of an hour, he needs to work at least 16 hours at the tutoring center.

Step 4 ：However, Jordan can only work a total of 40 hours a week. Since he has already worked 10 hours at the grocery store, he can only work \(40 - 10 = 30\) hours at the tutoring center.

Step 5 ：Therefore, the appropriate number of hours spent working at the tutoring center is the minimum of 16 and 30, which is 16.

Step 6 ：Final Answer: The appropriate number of hours spent working at the tutoring center is \(\boxed{16}\) hours.