Proportion — Solutions
Full worked solutions, with method and final answer for every part.
Question 1
(a)y = kx², so 18 = k(3²) = 9k, giving k = 2.
y = 2x²
(b)Substitute x = 5 into y = 2x².
y = 2(25) = 50
Question 2
(a)p = k/q, so 9 = k/4, giving k = 36. Then p = 36/6.
p = 6
Question 3
(a)y = k√x, so 12 = k√9 = 3k, giving k = 4. Then y = 4√25.
y = 4 × 5 = 20
Question 4
(a)F = k/r², so 20 = k/4, giving k = 80. Then F = 80/16.
F = 5
Question 5
(a)p = kq³, so 40 = k(2³) = 8k, giving k = 5. Then p = 5(3³).
p = 5 × 27 = 135
Question 6
(a)More workers complete the same job in less time (assuming equal work rate), so as one quantity increases the other decreases — this is inverse proportion.
Inversely proportional — more workers means less time needed
Question 7
(a)p=kq, so 20=4k, k=5; p=5×9.
p = 45
Question 8
(a)y=k/x, so 8=k/5, k=40; y=40/10.
y = 4
Question 9
(a)z=kw², so 27=9k, k=3; z=3×25.
z = 75
Question 10
(a)Two quantities are in direct proportion if their ratio stays constant — as one increases, the other increases by the same factor.
Their ratio stays constant; both increase or decrease by the same factor
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