Theory question 110
VariationThe cost of maintaining a school is partly constant and partly varies as the number of pupils. With 50 pupils, the cost is $15,705.00 and with 40 pupils, it is $13,305.00. (a) Find the cost when there are 44 pupils. (b) If the fee per pupil is $360.00, what is the least number of pupils for which the school can be run without loss?
Show the model answer
Model answer
Let C = a + kn.
a + 50k = 15705 and a + 40k = 13305. Subtract: 10k = 2400, k = 240; a = 15705 − 12000 = 3705.
(a) C = 3705 + 240 × 44 = $14,265.00.
(b) Need 360n ≥ 3705 + 240n, so 120n ≥ 3705 and n ≥ 30.9. Least number = 31 pupils.
Explanation
'Partly constant and partly varies' means C = a + kn.