Find the Unknowns

Class 7 Maths · Chapter 15: Finding the Unknown · NCERT Ganita Prakash section P2 7.1

Learn

Kabir's balance has 3 identical boxes and 2 kg on one pan and 14 kg on the other, and it balances. Take 2 kg off both pans: 3 boxes balance 12 kg, so one box is 4 kg. Writing x for a box: 3x + 2 = 14. A statement that two expressions are equal is an equation; the value that makes it true is its solution.

3x + 2 = 14 → 3x = 12 → x = 4

Boxes on both sides: 5 boxes + 3 kg balance 2 boxes + 15 kg. Take 2 boxes off each pan: 3 boxes + 3 kg = 15 kg. Take off 3 kg: 3 boxes = 12 kg, so a box is 4 kg. Whatever you do, do it to both sides and the balance stays level.

5x + 3 = 2x + 15 → x = 4

Matchsticks: a row of triangles uses 3, 5, 7, 9 … sticks, so position n needs 2n + 1. Which position uses exactly 99 sticks? Solve 2n + 1 = 99: 2n = 98, n = 49. Can it use 200 sticks? 2n = 199 has no whole-number solution (2n + 1 is always odd), so no. A statement that two expressions are equal is an equation, with a left-hand side (LHS) and right-hand side (RHS).

2n + 1 = 99 → n = 49

Checking a solution: put the value back. For 3x + 2 = 14, x = 4 gives 3 × 4 + 2 = 14 ✓, but x = 5 gives 17 ✗. Many equations have the same solution: 2x = 8, x + 6 = 10 and 3x − 2 = 10 are all solved by x = 4.

Explore: weigh a box.

1. 3 boxes + 2 kg balance 14 kg. Set the weight of one box.
2. 4 boxes + 1 kg balance 1 box + 25 kg. Set one box.

Remember

• An equation says two expressions are equal; its solution makes it true.
• Like a balance: do the same thing to both sides.

Quick check

Which value of n solves 3n + 1 = 31?

1. 10
2. 11
3. 30
4. 9

Think about it

A brick weighs 1 kg more than half of itself. How heavy is it?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.