Question

Machine at a manufacturing plant can make 16 of item A per hour or 20 of item B per hour. The machine runs for 24 hours a day. Yesterda

the machine made 434 total items. How many hours did item A run and how many hours did item B run on the machine?
Part A: Write a system of equations to represent this scenario.
write a system of equations to represent this scenario

Answer 1

A + B = 24

16A + 20B = 434

Explanation:

To write a system of equations for this scenario, let's say that A represents the number of hours machine A ran, and B represents the number of hours machine B ran.

The first equation will be:

A + B = 24

because the total number of hours ran is 24.

The second equation will be:

16A + 20B = 434

because the total number of items made is 434.

A + B = 24

16A + 20B = 434

First solve for one variable, and let's just do A.

Using the first equation, A + B = 24, A is equal to 24 - B.

Substitute this value to the second equation.

16 (24 - B) + 20B = 434

384 - 16B + 20B = 434

4B = 50

B = 12.5

Now use this value of B to find the value of A.

A + 12.5 = 24

A = 11.5

Machine A ran for 11.5 hours, and Machine B ran for 12 hours.