JAMB Mathematics Past Questions & Answers - Page 46

a Δ b = a + 3b + 2 (3 Δ 2) Δ 5 = (3 + 3(2) + 2) Δ 5 = 11 Δ 5 = 11 + 3(5) + 2 = 28

Education = $\frac{15}{100} \times N 50,000$

= N 7,500

Food = N 13,600

Electricity = $\frac{3}{100} \times N 50,000$

= N 1,500

Leftover : N (50,000 - (7,500 + 13,600 + 1,500))

= N 27,400

Since A(x, y) is the point of equidistance between B and C, then 

AB = AC

(AB)$^2$ = (AC)$^2$

Using the distance formula, 

(x - 0)$^2$ + (y - 2)$^2$ = (x - 2)$^2$ + (y - 1)$^2$

x$^2$ + y$^2$ - 4y + 4 = x$^2$ - 4x + 4 + y$^2$ - 2y + 1

x$^2$ - x$^2$ + y$^2$ - y$^2$ + 4x - 4y + 2y = 5 - 4

4x - 2y = 1

Let the number of days worked by the assistant = t

∴∴ The bricklayer worked (t + 10) days.

1500(t + 10) + 500(t) = N 95,000

1500t + 15,000 + 500t = N 95,000

2000t = N 95,000 - N 15,000

2000t = N 80,000

t = 40 days

∴∴ The assistant worked for 40 days and received N (500 x 40)

= N 20,000

$25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{-1}$

$(5^2)^{(1 - x)} \times 5^{(x + 2)} \div (5^{-3})^x = (5^4)^{-1}$

$5^{2 - 2x} \times 5^{x + 2} \div 5^{-3x} = 5^{-4}$

$5^{(2 - 2x) + (x + 2) - (-3x)} = 5^{-4}$

Equating bases, we have

$2 - 2x + x + 2 + 3x = -4$

$4 + 2x = -4 \implies 2x = -4 - 4$

$2x = -8$

$x = -4$