JAMB 1985 · UME · Q16

Variation

In a restaurant, the cost of providing a particular type of food is partly constant and partly inversely proportional to the number of people. If the cost per head for 100 people is 30k and the cost for 40 people is 60k, find the cost for 50 people.

Worked solution (try it first)

Partly constant and partly inversely proportional to the number $n$ : $C = a + \dfrac{b}{n}$ , with $C$ in kobo.
$n = 100$ : $a + \frac{b}{100} = 30$ .
$n = 40$ : $a + \frac{b}{40} = 60$ .
Subtract: $\frac{b}{40} - \frac{b}{100} = 30$ , so $\frac{3b}{200} = 30$ and $b = 2000$ .
Then $a = 30 - 20 = 10$ .
For 50 people the varying part is $\frac{2000}{50} = 40$ , so $C = 10 + 40 = 50$ k, option D.

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