Unit 11 · Algebraic / Equation Reasoning
Farmer's Goats — Simultaneous Equations
Lesson 1 of 4
A farmer, some goats, two possible outputs — this is a classic two-equation word problem in disguise. Name your unknowns, write the equations, subtract.
Two-variable word problems from real-life contexts (animals, products, items) appear regularly in the easy-to-medium band of official NSW papers — instantly recognisable once you spot the two unknowns.
The examiner checks whether you can translate "total items" and "total output" into two simultaneous equations, then solve by elimination rather than trial-and-error on the answer choices.
A total count of objects is split into two groups with different outputs (e.g. 1 kid vs 2 kids). You are given the total objects and the total output, and asked to find the size of one group.
Best approach: Step 1: find the active group size (subtract the "inactive" ones). Step 2: write x + y = total active and x + 2y = total output. Step 3: subtract equation 1 from equation 2 to get y instantly. Step 4: find x = total active − y. Step 5: verify by checking total output.
Question
A farmer has 245 female goats.
This year all but 9 of them have had kids.
None of them have had more than two kids.
357 kids have been born in total.
How many of the goats have had one kid only?
Select an answer to see the explanation.
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