Question

In a factory there are three machines, A, B, and C. When all three machines are working, they produce 287 bolts per hour. When only machines A and C are working, they produce 197 bolts per hour. When only machines A and B are working, they produce 202 bolts per hour. How many bolts can each machine produce per hour?

Answer 1

Let's assign variables to the number of bolts each machine produces per hour. Let's say machine A produces x bolts per hour, machine B produces y bolts per hour, and machine C produces z bolts per hour.

We have the following information from the problem:

When all three machines are working, they produce 287 bolts per hour:
x + y + z = 287 ................(1)

When only machines A and C are working, they produce 197 bolts per hour:
x + z = 197 ....................(2)

When only machines A and B are working, they produce 202 bolts per hour:
x + y = 202 ....................(3)

We now have a system of three equations with three variables, which we can solve to find the values of x, y, and z.

Subtracting equation (2) from equation (1), we get:
(x + y + z) - (x + z) = 287 - 197
x + y + z - x - z = 90
y = 90 ......................(4)

Subtracting equation (3) from equation (1), we get:
(x + y + z) - (x + y) = 287 - 202
x + y + z - x - y = 85
z = 85 ......................(5)

Substituting the values of y = 90 and z = 85 into equation (1), we get:
x + 90 + 85 = 287
x + 175 = 287
x = 287 - 175
x = 112 .....................(6)

So, machine A produces 112 bolts per hour, machine B produces 90 bolts per hour, and machine C produces 85 bolts per hour.