WAEC Mathematics Past Questions & Answers - Page 131

6 = \(\frac{1}{3}x\) = 1 + 2x

6 = 1 = \(\frac{2x}{1} - \frac{x}{3}\)

5 = \(\frac{6x - x}{3} = \frac{5x}{3}\)

5 = \(\frac{5x}{3}\)

3 x 5 = 5x

15 = 5x

x = \(\frac{15}{5}\)

= 3

P = {1, 2, 3, 4, 5, 6}; Q = {3, 4, 5, 6, 7, 8, 9}

P \(\cap\) Q) = {2, 3, 4, 5, 6}

n(P \(\cap\) Q) = 5

%Zinc + %Copper = 100%

65% + %Copper = 100%

%Copper = 100% - 65% = 35%

%Copper = \(\frac{\text{Mass of % Copper}}{\text{Mass of Casting}}\) x 100%

Mass of Casting = \(\frac{147}{35}\) x 100%

= 420g

Let the no. be x and x + 1

x + (x + 1) = \(\frac{5}{6}\) of x(x + 1)

2x + 1 = \(\frac{5}{6}\) x(x + 1)

6(2x + 1) = 5x² + 5x

12x + 6 = 5x² + 5x

5x² + 5x - 12x - 6 = 0

5x² - 7x - 6 = 0

5x² - 10x + 3x - 6 = 0

5x(x - 2) + 3(x - 2) = 0

(5x + 3)(x - 2) = 0

(5x + 3)(x - 2) = 0

(5x + 3) = 0

x - 2 = 0

for (5x + 3) = 0

5x = -3

x = \(\frac{-3}{5}\) (Imposible since x is a whole number)

x - 2 = 0

x = 2

x = \(\frac{-3}{5}\)(Impossible since x is a whole number)

x - 2 = 0

x = 2

The numbers are x = 2

x + 1 = 2 + 1

= 3

1\(\frac{1}{2} + 2\frac{1}{3} \times \frac{3}{4} - \frac{1}{2}\)

\(\frac{3}{2} + \frac{7}{3} \times \frac{3}{4} - \frac{1}{2} = \frac{3}{2} + \frac{7}{4} - \frac{1}{2}\)

= \(\frac{6 + 7 - 2}{4} = \frac{11}{4}\)

= 2\(\frac{3}{4}\)