KBAT Problems
KBAT Problem: Two Unknowns in a Real Situation
A KBAT problem where a real situation gives two conditions and you solve simultaneous equations to answer it.
Name the unknowns
Two people’s ages, or two item prices, are linked by two facts. Let each unknown be a letter, turn each fact into an equation, and you have a pair to solve.
Defining the unknowns clearly is the step that keeps the working honest.
Understand the problem
An original two-unknown problem. At a stall, 3 curry puffs and 2 drinks cost RM11, while 5 curry puffs and 4 drinks cost RM20.
Each price is unknown, and one purchase alone cannot fix both, so you need two equations. Naming the unknowns clearly, let a puff cost x and a drink cost y, is what turns the words into solvable maths.
Plan and solve
- Let x = price of a curry puff, y = price of a drink (in RM).
- Form the equations: 3x + 2y = 11 … (1) and 5x + 4y = 20 … (2).
- Multiply (1) by 2: 6x + 4y = 22 … (3).
- Subtract (2) from (3): x = 22 − 20 = 2.
- Substitute into (1): 3(2) + 2y = 11 → 2y = 5 → y = 2.50. So a puff is RM2 and a drink RM2.50.
Check and a variant
Check in equation (2): 5(2) + 4(2.50) = 10 + 10 = 20 ✓, so the prices are consistent with both conditions. A twist: the examiner then asks the cost of 4 puffs and 3 drinks, that is 4(2) + 3(2.50) = 8 + 7.50 = RM15.50.
Once the two unknowns are found, any follow-up combination is a quick substitution rather than new equations.
Frequently asked questions
How do I know a problem needs simultaneous equations?
When there are two unknowns and two separate conditions linking them, and no single condition pins either value on its own. Two different purchases, each giving a total, is the classic sign.
You set up one equation per condition, then solve them together so both unknowns satisfy both statements at once.
Should I use elimination or substitution?
Either works; pick whichever needs less rearranging. Elimination is neat when multiplying one equation makes a variable's coefficients match, as here.
Substitution is easier when one equation already has a variable by itself. The marks are the same, what matters is a correct, clearly shown method and both values at the end.
Why check in the other equation?
Because your working satisfied the equation you solved with by construction, so it cannot catch an error there. Substituting the answers into the untouched equation is an independent test, if it balances, both conditions hold and the prices are right.
It is a fast way to catch a slip before you lose marks.