Linear Equations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
4. Two numbers are in the ratio 5 : 8. When 9 is added to each of them, the ratio becomes 2 : 3. Find the smaller number.
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Answer: D) 45
Let the numbers be 5x and 8x. Then 8x+95x+9=32 → 3(5x + 9) = 2(8x + 9) → 15x + 27 = 16x + 18 → x = 9, so the smaller number is 5x = 45. Check: 54 : 81 = 2 : 3. The trap 9 is the value of x (not a number in the ratio) and 72 is the larger number.
5. Solve 5(x − 1) − 2(x + 3) = 2(x − 4) + 7.
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Answer: C) 10
Open every bracket: 5x − 5 − 2x − 6 = 2x − 8 + 7, so 3x − 11 = 2x − 1 and x = 10. Check: 5(9) − 2(13) = 45 − 26 = 19 and 2(6) + 7 = 19. Writing −2(x + 3) as −2x + 6 — failing to carry the minus onto the 3 — gives 3x + 1 = 2x − 1 and the trap −2.