Mathematics
Linear equations
Class 7
Intermediate
About 20 min
Premium
Solving equations: the shopkeeper's balance
Rice bags of unknown weight sit on a taraju. Take weights off both pans and share them out to find what one bag weighs.
Core concept
An equation stays balanced when the same thing is done to both sides
Topic: Linear equations
A shopkeeper's balance (taraju) is level when both pans hold the same weight, just as the two sides of an equation are equal. On the left pan are some rice bags that each weigh x kg, plus a few loose 1 kg weights; the right pan holds only 1 kg weights. 3x + 2 = 11 means 3 bags and 2 kg balance 11 kg. To find x, we may do anything we like, as long as we do the same to both pans: take the same weight off both, or share both pans into the same number of equal groups. The balance then stays level.
What you will learn
- Write an equation from a balance.
- Keep an equation balanced by doing the same operation to both sides.
- Solve equations of the form ax + b = c.
Before you start
- Subtract and divide small whole numbers.
Materials
- Small bags of rice of equal weight and 1 kg weights
Equipment
- A two-pan balance (taraju)
Procedure
- Tap a loose 1 kg weight on the left pan to take 1 kg off both pans; tap ↩ to put one back.
- When only bags are left, tap ÷ + to share both pans into as many equal groups as there are bags.
- Tap the puzzle card for the next puzzle, and solve each one.
- Switch to taking weights off the left pan only, and record what happens to the balance.
How this simulation is simplified
- Every rice bag in a puzzle has the same weight.