Answer:
They will coincide on the 84th day.
Step-by-step explanation:
Evaluating the details provided.
The health inspector comes every 7 days, while the fire inspector visits every 12 days.
Part (A) Create a table for the next 4 visits of each inspector.
The necessary table is as follows:
Health inspector: 7, 14, 21, 28
Fire inspector: 12, 24, 36, 48
Part (B) After how many days will both inspectors be present on the same day?
To solve this, we calculate the LCM of both numbers as follows:
7= 1×7
12=2×2×3
The LCM then is: 2×2×3×7=84
As a result, they will meet on the 84th day.