Question

A company manufactures three types of wooden chairs: the Kitui, the Goa, and the Santa Fe. To make a Kitui chair requires 1 hour of cutting time, 1.5 hours assembly time, and 1 hour of finishing time. A Goa chair requires 1.5 hours of cutting time, 2.5 hours of assembly time and 2 hours of finishing time. A Santa Fe chair requires 1.5 hours of cutting time, 3 hours of assembly time, and 3 hours of finishing time. If 41 hours of cutting time, 70 hours of assembly time, and 58 hours of finishing time were used one week, how many of each type of chair were produced.

Answer 1

Let k = number of Kitui chairs made, g = number of Goa chairs made, and s = number of Sante Fe chairs made. Let's start with cutting time. We know it took 41 hours to cut for all three chairs so....\[1k+1.5g+1.5s=41\]Likewise we can write a similar equation for the assembling time and for the finishing time. Then there are three equations and three unknowns. By substitution and rearranging , we can solve for, k, g, and s.

Answer 2

I have the equations:
k+1.5g+1.5s=41
1.5k+2.5g+3s=70
k+2g+3s=58

But when I do system of equations I get no solution, but the answer is supposed to be:
14 Kitui chairs, 10 Goa chairs, 8 Santa Fe chairs.

Answer 3

give me a moment

Answer 4

Can you check whether you copied the problem correctly?

Answer 5

It's correct, I've checked the problem multiple times, so I didn't know if I was making an error by getting no solution every time. But it might be a teacher error.

Answer 6

Yea, it might be. When I plug the answers back into the equations, they don't work but I don't think I set the equations up incorrectly. Hmmmmm......

Answer 7

Yeah, I had the same problem, so I thought it might be a small error on my part but I guess not. Thank you for your help! :)

Answer 8

you're welcome