Machine-rate scaling: 6 identical machines produce 270 bottles per minute. At the same constant rate, how many bottles will 10 such machines produce in 4 minutes?

Introduction / Context:
When identical machines work at a constant rate, output scales directly with both the number of machines and the time. Convert to per-machine output and then multiply up to the new count and duration.

Given Data / Assumptions:

• 6 machines ⇒ 270 bottles/minute.
• All machines are identical; rates are constant.
• Find output for 10 machines in 4 minutes.

Concept / Approach:
Per-machine rate = total rate / number of machines. New total = per-machine rate * new machines * new time. Ensure units (minutes) are consistent.

Step-by-Step Solution:

Verification / Alternative check:
Proportionality: scaling machines by 10/6 and time by 4 multiplies output by (10/6)*4 = 6.666… ⇒ 270 * 6.666… = 1800, same result.

Why Other Options Are Wrong:
1600, 1700, 2000, 2500 do not match the linear scaling from 270 bottles/min for 6 machines.

Common Pitfalls:
Forgetting to multiply by time, or dividing by the wrong machine count when computing per-machine rate.

Final Answer:
1800