Algebra 1 word problem. 4 students work part time.What restriction of hours for 4th?

[AnotherMime]

Four students are working part time on a projet. The first student works 14 hours per week. The second student works 16 hours per week, and the third student works 20 hours per week. The policy is that the average number of hours that the students work has to be less than 16 hours. What is the restriction for the number of hours that the fourth student can work?

 

[HopeWelch]

I would just set up an inequality...(Not an equation. proper math lingo?)

Average is total hours divided by the number of students.

So this to me looks like:

(14+16+20+x)/4 < 16

(50 + x)/4 < 16

50/4 + x/4 < 16

12.5 + x/4 < 16

x/4 < 3.5

x < 14

This means the 4th student must work less than 14 hours to stay below the 16 hour average.

 

[AnotherMime]

Problem Solved - Thank You HopeWelch

The first reply by JeffM was appreciated but the usage of \leq seemed to be beyond first year algebra. I had trouble understanding it. The reply by HopeWelch used basic algebra equations to set up and solve the problem. I understood HopeWelch's solution work and the answer. Thank you very much for your quick responses. It helped me alot. I hate not understanding a problem and being completely stuck.

 

[Mrspi]

The first reply by JeffM was appreciated but the usage of \leq seemed to be beyond first year algebra. I had trouble understanding it. The reply by HopeWelch used basic algebra equations to set up and solve the problem. I understood HopeWelch's solution work and the answer. Thank you very much for your quick responses. It helped me alot. I hate not understanding a problem and being completely stuck.

WE hate not understanding where a student is "stuck" on a problem. If one or more of us has NOT met your expectations for getting help here, it may very well be because you did not show us any work you had done, nor told us where you were stuck....

 

[AnotherMime]

Very Grateful - Assistance Exceeded My Expectations

Sorry, I must have miscommunicated what I was trying to convey in my last response. I think it was taken the wrong way. I am very grateful for the quick assistance that I received on my math problem. I received two different methods of working the problem. That was great. The assistance that I received on this thread far exceeded my expectations. My first time to use it. And I will recommend it to others who need help. Thank you very much.

 

[HopeWelch]

Sorry if I offended anyone but I'm just a math minor who has gotten help here from so many people already. I appreciate it sooooo much that when I see a rare one or two that I can actually help with I try and return the favor...