Algebra 6
3 marks · NormalA factory produces widgets. The number of widgets, , produced is directly proportional to the number of workers, , employed.
On a certain day, 50 workers produce 600 widgets. Write the formula connecting and .
How many widgets would 90 workers produce?
How many workers are needed to produce 960 widgets?
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(a) N = 12w
(b) 1080
(c) 80
Common mistakes: Solving the wrong variable; Not converting proportions correctly
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · States or derives N = 12w correctly.
A1 (b) · 1 mark · Calculates N for w = 90 as 1080. (follow-through)
A2 (c) · 1 mark · Finds number of workers for N = 960 as 80. (follow-through)
Worked solution
Let N = kw. 600 = k × 50 ⇒ k = 12. So N = 12w.
b) For w = 90: N = 12 × 90 = 1080.
c) For N = 960: 960 = 12w ⇒ w = 80.