WAEC 2021 · Paper 2 · Q6✱✱

(a)
The sum of two numbers is 91. If one-quarter of one of the numbers added to one-fifth of the other is 21, find the numbers.
Separate values with commas, e.g. 3, −2
(b)
If $2$ and $-\frac58$ are the roots of the quadratic equation $px^2 + qx + r = 0$ , find the values of $p$ , $q$ and $r$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)

Let the numbers be $x$ and $y$ .
Their sum is 91: $x + y = 91$ (1).
A quarter of one plus a fifth of the other is 21: $\frac x4 + \frac y5 = 21$ .
Multiply by 20: $5x + 4y = 420$ (2).
From (1), $y = 91 - x$ , so $5x + 4(91 - x) = 420$ .
Then $5x + 364 - 4x = 420$ and $x = 56$ .
So $y = 35$ .
The numbers are 56 and 35.

(b)

The root $x = 2$ gives the factor $(x - 2)$ .
The root $x = -\frac58$ gives $8x = -5$ , so the factor $(8x + 5)$ .
The equation is $(x - 2)(8x + 5) = 0$ .
Expand: $8x^2 + 5x - 16x - 10 = 8x^2 - 11x - 10$
$= 0$ .
So $p = 8$ , $q = -11$ and $r = -10$ .

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