Question

How to set the answer up

Answer 1

Let s and g represents the numbers of suits and gowns produced.

The number of zippers used is 2s+g.

The number of buttons used is 5s+8g.

In order to use all of the available zippers and buttons, we must have ...

• 2s + g = 171
• 5s + 8g = 576

Cramer's rule tells you the solution to the system

• ax +by = c
• dx +ey = f

Is given by

• x = (bf-ey)/(bd-ea)
• y = (cd-fa)/(bd-ea)

Using this rule on the equations for zippers and buttons, we have

... s = (1·576 -8·171)/(1·5 -8·2) = -792/-11 = 72

... g = (171·5 -2·576)/-11 = -297/-11 = 27

72 suits and 27 gowns can be made from available zippers and buttons.