WAEC 2016 · Paper 2 · Q8

(a)
In the diagram, $\angle KLM = x$ , $\angle LMK = y$ , $\angle KJH = r$ and $\angle KGF = 110^\circ$ . If $2x = r = y$ , find the value of $x$ .
(b)
Ten boys and twelve girls collected donations for a project. The total amount collected by the boys was ₦600.00 greater than that collected by the girls. If the average collection of the boys was ₦100.00 greater than the average collection of the girls, how much was collected by the two groups?

Worked solution (try it first)

$\angle JKM$ is an exterior angle of $\triangle KLM$ , so it equals the sum of the two opposite interior angles: $\angle JKM = x + y$ .
Then $\angle KGF = 110^\circ$ is an exterior angle of $\triangle JKG$ , so $(x + y) + r = 110^\circ$ .
Since $y = r = 2x$ : $x + 2x + 2x = 110^\circ$ , so $5x = 110^\circ$ and $x = 22^\circ$ .

Let the boys collect ₦ $B$ in total and the girls ₦ $G$ .
The boys collected ₦600 more: $B - G = 600$ (1).
The boys' average is $\frac{B}{10}$ and the girls' is $\frac{G}{12}$ .
The boys' average is ₦100 more: $\frac{B}{10} - \frac{G}{12} = 100$ .
Multiply by 60: $6B - 5G = 6000$ (2).
From (1), $B = G + 600$ .
Substitute into (2): $6(G + 600) - 5G = 6000$ , so $G + 3600 = 6000$ and $G = 2400$ .
Then $B = 3000$ .
Together they collected $3000 + 2400 =$ ₦5,400.00.