Question

It takes a total of 78 hours to build four bed frames, a bookcase, and three chairs. It takes 108 hours to build six bed frames and four chairs. It takes 74 hours to build three bed frames, five bookcases, and two chairs.

Answer 1

9514 1404 393

Answer:

• bed frame: 14 hours
• bookcase: 4 hours
• chair: 6 hours

Explanation:

Perhaps you want to know how many hours it takes to build each item.

If we let f, b, c represent the number of hours for a frame, bookcase, and chair, respectively, the equations can be written as ...

• 4f +b +3c = 78
• 6f +0b +4c = 108
• 3f +5b +2c = 74

Your graphing calculator or an on-line matrix solver can find the reduced row-echelon form of the augmented matrix ...

`\left[\begin{array}c4&1&3&78\\6&0&4&108\\3&5&2&74\end{array}\right]`

That result will tell you ...

(f, b, c) = (14, 4, 6)

It takes 14 hours to build a bed frame, 4 hours to build a bookcase, and 6 hours to build a chair.