Theory question 106
Logarithms(a) If log 5 = 0.6990, log 7 = 0.8451 and log 8 = 0.9031, calculate: log ((35 × 49)/(40 ÷ 56))
(b) 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 (i) value of x; (ii) ratio of the number of children to the number of adults; (iii) average amount paid per person; (iv) percentage profit if the organisers spent D720 on the show.
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(a) (35 × 49)/(40 ÷ 56) = (5 × 7)(72)(8 × 7)/(8 × 5) = 74.
log 74 = 4 × 0.8451 = 3.3804.
(b)(i) 2x + 5(x + 60) = 1280 → 7x = 980 → x = 140.
(ii) Children : adults = 140 : 200 = 7 : 10.
(iii) 1280 ÷ 340 ≈ D3.76 per person.
(iv) Profit = 1280 − 720 = D560; percentage = 560/720 × 100% ≈ 77.8%.
Break each number into prime factors before using the logs.