WAEC 2019 · Paper 2 · Q5

(a)
The cost of dinner for a group of tourists is partly constant and partly varies as the number of tourists present. It costs $740.00 when 20 tourists were present and $960.00 when the number of tourists increased by 10. Find the cost of the dinner when only 15 tourists were present.

Worked solution (try it first)

"Partly constant and partly varies as the number of tourists": $C = a + bn$ , where $C$ is the cost in dollars and $n$ the number of tourists.
20 tourists: $a + 20b = 740$ .
The number increased by 10, so 30 tourists: $a + 30b = 960$ .
Take the first equation from the second: $10b = 220$ , so $b = 22$ .
Then $a = 740 - 20 \times 22 = 740 - 440 = 300$ .
So $C = 300 + 22n$ .
For 15 tourists: $C = 300 + 22 \times 15 = 300 + 330 = 630$ .
The dinner costs $630.00.