From a puzzle to a line

A cycle shop charges ₹15 for each patch. A patch is a rubber piece that seals a hole. Fitting the tube costs ₹25. The bill is ₹85. How many patches? Call that number p.

Two amounts, two jobs

The bill is for 4 patches. Check: 15 × 4 + 25 = 85.

Which amount repeats for each patch? The ₹15. So it goes with the letter: 15p. That means 15 times p.

What happens once for the whole job? The ₹25 fitting charge. It stands alone.

Together: 15p + 25 = 85. Take 25 off both sides: 15p = 60, because 85 − 25 = 60. Share both sides by 15: p = 4, because 60 ÷ 15 = 4.

Rule: The amount that repeats goes with the letter. The amount charged once stands alone.

Try the lab to finish this lesson.