What is the production rate of machine B in a factory where three machines produce 287 cases, A and C produce 197, and A and B produce 202?

To determine the production rate of machine B, we can set up a system of equations based on the information provided:

Let the production rates of machines A, B, and C be represented as ( a ), ( b ), and ( c ) respectively.

From the problem, we have the following equations:

1. ( a + b + c = 287 ) (combined production of all three machines),

2. ( a + c = 197 ) (combined production of machines A and C),

3. ( a + b = 202 ) (combined production of machines A and B).

We can now solve for the values of ( b ) (the production rate of machine B) using these equations.

From the second equation, we can solve for ( a ):

[

a + c = 197 \implies c = 197 - a

]

Next, substitute this value of ( c ) into the first equation:

[

a + b + (197 - a) = 287

]

This simplifies to:

[

b + 197 = 287

]

[

b = 287 - 197

]

[

b = 90

]