WAEC 2022 · Paper 2 · Q2✱✱

(a)
The total cost of 2 packed lunches and 3 packed breakfasts is $40.00. The cost of 2 packed lunches is $12.00 less than the cost of a packed breakfast. Find the cost of a packed breakfast.
(b)
Find the quadratic equation whose roots are $-\frac13$ and $5$ .
Show the answer
$3x^2 - 14x - 5 = 0$

Worked solution (try it first)

(a)

Let a packed lunch cost $ $x$ and a packed breakfast $ $y$ .
The total cost: $2x + 3y = 40$ (1).
Two lunches cost $12 less than one breakfast: $2x = y - 12$ (2).
Substitute (2) into (1): $(y - 12) + 3y = 40$ .
So $4y = 52$ and $y = 13$ .
A packed breakfast costs $13.00.

(b)

The root $x = -\frac13$ gives $3x = -1$ , so the factor $(3x + 1)$ .
The root $x = 5$ gives the factor $(x - 5)$ .
The equation is $(3x + 1)(x - 5) = 0$ .
Expand: $3x^2 - 15x + x - 5 = 0$ , so $3x^2 - 14x - 5 = 0$ .

Report a problem with this question