WAEC 2009 · Paper 2 · Q6

(a)
If $\log 5 = 0.6990$ , $\log 7 = 0.8451$ and $\log 8 = 0.9031$ , evaluate $\log\left(\dfrac{35 \times 49}{40 \div 56}\right)$ .
(b)(i)
For a musical show, $x$ children were present. There were 60 more adults than children. An adult paid D5 and a child D2. If a total of D1280 was collected, calculate the value of $x$ .
(b)(ii)
Calculate the ratio of the number of children to the number of adults.
(b)(iii)
Calculate the average amount paid per person.
(b)(iv)
Calculate the percentage profit if the organisers spent D720 on the show.

Worked solution (try it first)

Write each number with factors 5, 7 and 8: $35 = 5 \times 7$ , $49 = 7 \times 7$ , $40 = 5 \times 8$ , $56 = 7 \times 8$ .
Dividing by $40 \div 56$ is multiplying by $\frac{56}{40}$ : the number is $\frac{5 \times 7 \times 7 \times 7 \times 7 \times 8}{5 \times 8} = 7^4$ .
So the log is $4\log 7 = 4 \times 0.8451 = 3.3804$ .