Question

It takes 56 hours to build three bed frames, a bookcase, and four chairs. It takes 66 hours to build four bed frames and six chairs. It takes 89 hours to build two bed frames, seven bookcases and three chairs. How many hours does it take to build one bed frame?

Answer 1

• 12 hours

Explanation:

Let the times be:

• Bed frame - f
• Bookcase - b
• Chair - c

We have following equations:

• 3f + b + 4c = 56
• 4f + 6c = 66
• 2f + 7b + 3c = 89

Simplify the second equation and subtract from the third one:

• 7b = 89 - 33
• 7b = 56
• b = 8

Replacing b in the first and third equations:

• 3f + 4c = 48
• 2f + 3c = 33

Four times the bottom equation and subtract the triple the one above:

• 8f - 9f = 4(33) - 3(48)
• f = 12

It takes 12 hours to build one bed frame