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. Which system of equations represents this situation?(1 point)
Responses

A+B+D=197A+C=202A+B=287
𝐴
+
𝐵
+
𝐷
=
197
𝐴
+
𝐶
=
202
𝐴
+
𝐵
=
287

A+B+C=197A+C=202A+B=287
𝐴
+
𝐵
+
𝐶
=
197
𝐴
+
𝐶
=
202
𝐴
+
𝐵
=
287

A+B+C=250A+C=197A+B=287
𝐴
+
𝐵
+
𝐶
=
250
𝐴
+
𝐶
=
197
𝐴
+
𝐵
=
287

A+B+C=287A+C=197A+B=202

Answer 1

To determine the system of equations that represents the situation with the machines A, B, and C, let's summarize the information provided:

1. When all three machines A, B, and C are working, they produce 287 bolts per hour.
2. When only machines A and C are working, they produce 197 bolts per hour.
3. When only machines A and B are working, they produce 202 bolts per hour.

We can define the terms as follows:
- Let \( A \) be the production rate of machine A.
- Let \( B \) be the production rate of machine B.
- Let \( C \) be the production rate of machine C.

From the information provided, we can write the following equations:

1. \( A + B + C = 287 \) (when all three machines are working)
2. \( A + C = 197 \) (when only machines A and C are working)
3. \( A + B = 202 \) (when only machines A and B are working)

Now, let's match this with the provided options:

- The correct system of equations is:
\[
A + B + C = 287
\]
\[
A + C = 197
\]
\[
A + B = 202
\]

Thus, the correct option is:
**A + B + C = 287, A + C = 197, A + B = 202.**