WAEC 2020 · Paper 2 · Q2

(a)
The cost of 3 cutlasses and 2 hoes is GH₵ 85.00. If the cost of 2 cutlasses and 3 hoes is GH₵ 90.00, calculate the total cost of a cutlass and a hoe.
(b)
If the graph of $y = k(x + 4)(x - 1)$ intersects the line $x = 0$ at $y = 24$ , find the value of $k$ .

Worked solution (try it first)

(a)

Let a cutlass cost GH₵ $c$ and a hoe GH₵ $h$ .
Then $3c + 2h = 85$ (1) and $2c + 3h = 90$ (2).
Add the two equations: $5c + 5h = 175$ , so $c + h = 35$ .
A cutlass and a hoe together cost GH₵ 35.00.
(Solving fully gives $c = 15$ and $h = 20$ .)

(b)

The line $x = 0$ is the $y$ -axis, so the graph passes through $(0, 24)$ .
Substitute: $24 = k(0 + 4)(0 - 1) = -4k$ .
So $k = -6$ .

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