Question

1(a) Given that (7−2x), 9, (5x+17) are consecutive terms of a Geometric Progression (G.P) with common ratio r>0, find the values of x.
(b) Two positive numbers are in the ratio 3:4. The sum of thrice the first number and twice the second number is 68. Find the smaller number.

Accepted Answer

(a) For a G.P, the common ratio is constant: 9/(7−2x) = (5x+17)/9. Cross-multiplying: (7−2x)(5x+17)=81. 35x+119−10x²−34x=81. −10x²+x+38=0. Dividing by −1: 10x²−x−38=0. Using the quadratic formula or factoring: 10x²−20x+19x−38=0 → 10x(x−2)+19(x−2)=0 → (10x+19)(x−2)=0. So x=−19/10 or x=2.

(b) Let the numbers be x and y, with x:y=3:4, so x=(3/4)y.
From the second statement: 3x+2y=68.
Substituting: 3(3/4)y+2y=68 → (9/4)y+2y=68 → (17/4)y=68 → y=16.
x=(3/4)(16)=12.
Therefore, the smaller number is 12.

WAEC Mathematics 2022 Theory — Question 1

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