(a) Fred bought a car for $5,600.00 and later sold... | WAEC SSCE - General Mathematics - 2019 (Essay)

Question 1 Report

(a) Fred bought a car for $5,600.00 and later sold it at 90% of the cost price. He spent $1,310.00 out of the amount received and invested the rest at 6% per annum simple interest. Calculate the interest earned in 3 years.

(b) Solve the equations 2$^x$(4$^{-7}$) = 2 and 3$^{-x}$(9$^{2y}$) = 3 simultaneously.

Answer

(a) Simple interest earned

Selling price $= 90\%$ of $\$5{,}600.00 = \dfrac{90}{100}\times 5600 = \$5{,}040.00$.

Amount left to invest $= 5040 - 1310 = \$3{,}730.00$.

Simple interest $I=\dfrac{PRT}{100}=\dfrac{3730\times 6\times 3}{100}=\dfrac{67140}{100}=\$671.40$.

The interest earned in 3 years is $\$671.40$.

(b) Simultaneous indices

(The equations are read as $2^{x}\!\cdot 4^{-y}=2$ and $3^{-x}\!\cdot 9^{2y}=3$; a single-variable first equation would not give a genuine simultaneous system.)

Equation 1: $2^{x}\cdot (2^{2})^{-y}=2^{1}\Rightarrow 2^{x-2y}=2^{1}\Rightarrow x-2y=1$.

Equation 2: $3^{-x}\cdot (3^{2})^{2y}=3^{1}\Rightarrow 3^{-x+4y}=3^{1}\Rightarrow -x+4y=1$.

Adding the two: $(x-2y)+(-x+4y)=1+1\Rightarrow 2y=2\Rightarrow y=1$.

Then $x-2(1)=1\Rightarrow x=3$.

$x=3,\ y=1$. Check: $2^{3}\cdot 4^{-1}=8/4=2$ and $3^{-3}\cdot 9^{2}=81/27=3$. $\checkmark$

Read lesson note on Representation Of Data (JAMB)

Read lesson note on Solution Of Linear Equations (WAEC)

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