KJSEA 2025 Maths Q6 — Algebraic Expressions (Number of Sheep)
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The Question
“Kiyappi's farm has 26 animals in total. There are X donkeys. The number of goats is twice the number of donkeys, and the rest of the animals are sheep. Write an expression that represents the number of sheep on the farm.”
Write down what you know
Start by naming each group of animals in terms of X. The number of donkeys is given directly as X. This is the unknown quantity the whole question is built around, so everything else should be written using it.
Express the goats in terms of X
The goats are twice the number of donkeys. In algebra the word twice means multiply by two, so we double the number of donkeys to get the number of goats.
Subtract the known groups from the total
The sheep are whatever animals are left over after counting the donkeys and the goats. Since the farm has 26 animals in total, we take the total and subtract both the donkeys and the goats to find what remains.
Collect the like terms
The two terms containing X can be combined because they are like terms. Adding one X and two X gives three X, and both are being subtracted, so together they subtract three X from the total.
Final Result
The number of sheep is 26 minus 3X, which is option A.
Why this method works
The method works because the total number of animals is simply the sum of the three groups: donkeys, goats and sheep. If donkeys are X and goats are twice that, 2X, then together they account for 3X animals. The sheep must make up the difference so that all three groups add back to 26, so the sheep count is the total minus that combined 3X. Combining the like terms X and 2X into 3X keeps the expression in its simplest form, which is exactly what the multiple-choice options are written in.
Test with X = 5: donkeys 5, goats 10, sheep = 26 - 15 = 11, and 5 + 10 + 11 = 26. It balances.