I am having trouble setting up the equations for this problem. I think that I am reading too much into it. Any help would be great. Thank you in advance.

As a business owner there are many decisions that you need to make on a daily basis, such as ensuring you reach the highest production levels possible with your company’s products. Your company produces two models of bicycles: Model A and Model B. Model A takes 2 hours to assemble, where Model B takes 3 hours to assemble. Model A costs $25 to make per bike where Model B costs $30 to make per bike. If your company has a total of 34 hours and $350 available per day for these two models, how many of each model can be made in a day?

* Solve the equations for the different bicycle models that can be made daily with the desired technique learned (graphing, substitution, elimination, matrix).

* Explain how to check your solution for both equations.

I would suggest simultaneous equation:
Let a be Model A
Let b be Model B

Equation for hours:
2a + 3b = 34 ----------------- I

Equation for costs
25a + 30b = 350 ------------- II

Multiply equation I by 10
20a +30b = 340 --------------III
25a + 30b = 350 --------------II

Deducting II from III, we get
-5a = -10
or a = 2

Substitute the value of a in equation I
2 x 2 + 3b = 34
3b = 34 - 4
b = 10

Check:

Hours
Model A 2 cycles x 2 hours = 4 hours
Model B 10 cycles x 3 hours = 30 hours
Total Hours 34

Costs
Model A 2 cycles x $25 = $50
Model B 10 cycles x $30 = $300
Total costs $350

Q.E.D.

rehmanvohra,
Thank you for your help. I had the answers 4 & 10, but could not figure out the equations for the check. Thank you again.

PSU FAN