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?

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?

• A. 85
• B. 90
• C. 112
• D. 100

Answer: (B)

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: \[ b + 197 = 287 \] \[ b = 287 - 197 \] \[ b = 90 \]

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

]