NECO 2024 · Paper 2 · Q7

(a)
Solve the equation $\dfrac{19}{12} - \dfrac{3}{4(x - 4)} = \dfrac56$ .
(b)
The cost of transportation is partly constant and partly varies as the distance covered. The cost is ₦1,025.00 when 220 km is covered and ₦1,345.00 when 300 km is covered. If the distance between Lagos and Kaduna is 982 km, find the cost of transportation (₦).

Worked solution (try it first)

(a)

Move the known fractions to one side: $\frac{3}{4(x - 4)} = \frac{19}{12} - \frac56$ .
With denominator 12, $\frac56 = \frac{10}{12}$ , so the right side is $\frac{9}{12} = \frac34$ .
Now $\frac{3}{4(x - 4)} = \frac34$ .
The tops are both 3, so the bottoms must be equal: $4(x - 4) = 4$ .
So $x - 4 = 1$ and $x = 5$ .

(b)

"Partly constant and partly varies as the distance" means $C = a + bd$ , where $C$ is the cost in naira and $d$ the distance in km.
From the two journeys: $a + 220b = 1025$ and $a + 300b = 1345$ .
Take the first from the second: $80b = 320$ , so $b = 4$ .
Then $a = 1025 - 220 \times 4 = 145$ .
So $C = 145 + 4d$ .
For 982 km: $C = 145 + 4 \times 982$
$= 145 + 3928$
$= 4073$ .
The cost is ₦4,073.00.

Report a problem with this question