Question

This table shows the running time, in hours, for each of the three widget producing machines over the course of three months. Find the number of widgets produced per hour by each machine. Let x1, x2, and x3 represent widgets produced per hour for each machine.

Answer 1

100 x1 + 130 x2 + 16 x3 = 4758

120 x1 + 180 x2 + 28 x3 = 6504

160 x1 + 190 x2 + 10 x3 = 6720

pt 2

x1 = 15

x2 = 21

x3 = 33

Explanation:

Answer 2

The number of widgets produced per hour by Machine A, B, and C is approximately 297, 54, and 672, respectively.

The task involves determining the number of widgets produced per hour by each of the three widget-producing machines (A, B, and C) based on the given running time and widgets produced data over three months.

To achieve this, we can set up a system of linear equations, where X1, X2, and X3 represent the widgets produced per hour by Machines A, B, and C, respectively. The linear system is derived from the information provided for each month, where the total running time for each machine multiplied by the widgets produced per hour should equal the total number of widgets produced.

Upon solving this system, we find that Machine A produces approximately 297 widgets per hour, Machine B produces around 54 widgets per hour, and Machine C produces about 672 widgets per hour. These values are derived by solving the system of equations and represent the production rates for each machine per hour based on the given data.