Question

Four machines A, B, C, D produce items in a ratio.
A produces 40 more than B.
C produces 20% more than A.
D produces half of B.
If total production is 860 items,
how many items did Machine C produce?

Hint:

When one value is defined as a percentage or offset of another, rewrite everything using a single variable. This keeps the total-sum equation simple and avoids mistakes.

Answer 1

Correct Answer: 269

Step 1: Write \(A=B+40\), \(D=0.5B\), and \(C=1.2A=1.2B+48\), all in terms of \(B\).
Step 2: Substitute into \(A+B+C+D=860\): \[ (B+40)+B+(1.2B+48)+0.5B=3.7B+88=860. \]
Step 3: Solve: \(3.7B=772 \implies B=\dfrac{7720}{37}\approx208.65\).
Step 4: Then \(A=B+40\approx248.65\), and \[ C=1.2A\approx\boxed{298.4 \text{ items}} \]
(Note: \(B\) itself is not a whole number, suggesting the given figures may not be fully consistent for whole-item production counts.)