Question

11) The Cost of maintaing a

school is party
Constant and partly varies as the number of
Pupils with 50 pupils the cost is $15705 with 40 pupils, it is $13305
find the cost when there are 44 pupils
B if the fee per pupil is 360 what is the
Least number of pupils for which the school can be run without loss
​

Answer 1

a). Cost of 44 pupils = $14265

b). Least number of pupils = 31

Explanation:

The given question is incomplete; here is the complete question.

The 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 run without a loss?

Let the equation representing the total cost of maintaining a school is,

C = ax + b

Where C = Total cost of maintaining a school

a = Fee per pupil

b = Fixed running cost

x = number of pupils

a). Cost of 50 pupils = $15705

Equation will be,

15705 = 50a + b -------(1)

Cost of 40 pupils = $13305

Equation will be,

13305 = 40a + b --------(2)

By subtracting equation (2) from equation (1),

15705 - 13305 = (50a + b) - (40a + b)

2400 = 10a

a = 240

From equation (1),

b = 3705

Equation representing the total cost will be,

C = 240x + 3705

If x = 44

C = 240(44) + 3705

C = $14265

b). If the fee per pupil 'a' = $360

Let the number of pupils = p

Total fee of 'p' pupils = $360p

Total cost to run the school will be = 3705 + 240p

For the school not to be in the loss,

360p ≥ 3705 + 240p

360p - 240p ≥ 3705

120p ≥ 3705

p ≥
`(3705)/(120)`

p ≥ 30.875

Therefore, to run the school without loss, number pupils should be at least 31.