WAEC 2018 · Paper 2 · Q11

(a)
If $\log_a(y + 2) = 1 + \log_a x$ , find $x$ in terms of $y$ .
(b)

Community Bibiani Amenfi Oda Wiawso Sankore

Timber production (tonnes) 600 900 1800 1500 2400

The table shows the distribution of timber production in five communities in a certain year. (i) Draw a pie chart to represent the information. (ii) What percentage of timber produced that year was from Amenfi? (iii) If a tonne of timber is sold at $560.00, how much more revenue would Oda community receive than Bibiani?
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)

Write 1 as $\log_a a$ : $\log_a(y + 2) = \log_a a + \log_a x$
$= \log_a(ax)$ .
The logs are equal, so $y + 2 = ax$ and $x = \frac{y + 2}{a}$ .

(b)(i)

The total is $600 + 900 + 1800 + 1500 + 2400 = 7200$ tonnes, and $360^\circ$ stands for 7200 tonnes, so each $1^\circ$ is 20 tonnes.
The sector angles: Bibiani $\frac{600}{20} = 30^\circ$ , Amenfi $45^\circ$ , Oda $90^\circ$ , Wiawso $75^\circ$ , Sankore $120^\circ$ (total $360^\circ$ ).
Draw them with a protractor and label each sector.

(ii)

Amenfi's share is $\frac{900}{7200} \times 100 = 12.5\%$ .

(iii)

Oda produced $1800 - 600 = 1200$ tonnes more than Bibiani, so it would receive $1200 \times \text{\textdollar}560 = \text{\textdollar}672,000$ more.

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