NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 7: Algebra - Problems and Solutions

Question 86

How to translate each sentence into an equation

Tip: Match words to the given letters (variables), then write the math in small steps.

(a) Perimeter of an equilateral triangle

1. An equilateral triangle has all three sides equal.
2. Each side is ( a ).
3. Perimeter means the sum of all sides.
4. So, perimeter ( p ) = ( a + a + a ).
5. ( a + a + a = 3 imes a ).
6. Therefore, ( p = 3a ).

(b) Diameter and radius of a circle

1. The radius is the distance from the center to the edge.
2. The diameter is the full width across the circle.
3. One diameter has two radii.
4. So, diameter ( d ) = ( 2 imes r ).
5. Therefore, ( d = 2r ).

(c) Selling price, cost price, and profit

1. Cost price is the amount paid to buy the item. Let it be ( c ).
2. Profit is the extra money earned. Let it be ( p ).
3. Selling price is what you sell it for. Let it be ( s ).
4. Selling price = cost price + profit.
5. So, ( s = c + p ).

(d) Amount, principal, and interest

1. Principal is the original money invested or borrowed. Let it be ( p ).
2. Interest is the extra money paid/earned. Let it be ( i ).
3. Amount is the total after adding interest. Let it be ( a ).
4. Amount = principal + interest.
5. So, ( a = p + i ).