Question

The cost of maintain a school is partly constant and partly varies .with 50 pupils the cost is 15705 and with 44 pupils the cost is 13305 find the cost when there are 40 pupils and if the fee per pupils is 360.00 what is the least number of pupils for which the school can run without a loss

Answer 1

Answer:

Let P represent the cost ; n, the number of pupils and k and c, constant terms.

∴P=k+cn∴P=k+cn

15705=k+50c...(1)15705=k+50c...(1)

13305=k+40c....(2)13305=k+40c....(2)

(1) - (2) :

2400=10c⟹c=240010=2402400=10c⟹c=240010=240

Put c = 240 in (1), so that

15705=k+(50)(240)15705=k+(50)(240)

15705=k+12000⟹k=370515705=k+12000⟹k=3705

P=3705+240nP=3705+240n ------ formula connecting price and number of pupils.

(a) When number of pupils, n = 44

P=3705+240(44)=3705+10560=$14265P=3705+240(44)=3705+10560=$14265

(b) For school not to be at loss:

360≥k+cn360≥k+cn

360n≥3705+240n360n≥3705+240n

360n−240n≥3705⟹120n≥3705360n−240n≥3705⟹120n≥3705

n≥3705120n≥3705120

n≥30.875n≥30.875

n≥31n≥31

The pupils should be 31 at least for the school not to run at loss.