Question

8(a) In the diagram above, ∠KLM=x°, ∠LMK=y°, ∠KJH=r° and ∠KGF=110°. 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?

Accepted Answer

(a) From ΔKJG: ∠KGJ=180°-110°=70° (angle on a straight line)
JKG is an exterior angle: x°+y°+r°+70°=180° (sum of opposite interior angles equals exterior angle theorem applied appropriately)
Since y°=r°=2x° (given): x°+2x°+2x°+70°=180°
5x°=180°-70°=110°
x°=22°

(b) Let x = amount collected by boys, y = amount collected by girls
x = y+600 ......(i)
Average collected by boys = x/10, average collected by girls = y/12
x/10 = y/12 + 100 ......(ii)
Substituting (i) into (ii): (y+600)/10 = y/12+100
Multiply through by 60: 6(y+600)=5y+6000
6y+3600=5y+6000
y=2400
x=2400+600=3000
Total collected by the two groups = 3000+2400 = 5400

WAEC Mathematics 2016 Theory — Question 8

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