For 3 shifts, the worker collects 14 devices. He collected a batch of devices in 18 shifts. How many devices were there in this batch?

Step 1: Interpret the Problem and Set Up a Proportion
In this problem, we know that 14 devices were collected in 3 shifts. We are trying to find the number of devices that were collected over 18 shifts.
When we set up the proportion, the units must match. Since we are dealing with devices per shift, the number of devices will be in the numerator and shifts will be in the denominator.
What is missing is the number of devices.
So we have:
\(\frac{\mathrm{14 devices}}{\mathrm{3 shifts}} = \frac{\mathrm{x devices}}{\mathrm{18 shifts} }\)
\(\frac{\mathrm{14} }{\mathrm{3} } = \frac{\mathrm{x} }{\mathrm{18} }\)
Step 2: Cross Multiply & Solve the Equation
To find the X, we multiply one denominator by the opposite numerator.
14 × 18 = 3 × x
This gets simplified to:
252 = 3x
Now we can solve for x:
\(\frac{\mathrm{252} }{\mathrm{3} } = \frac{\mathrm{3x} }{\mathrm{3} }\)
\(252 ÷ 3 = 84\)
x = 84
There were 84 devices in the batch.