Theory question 109
Progressions(a) The first term of an Arithmetic Progression (AP) is −8. If the ratio of the 7th term to the 9th term is 5 : 8, find the common difference of the AP.
(b) A trader bought 30 baskets of pawpaw and 100 baskets of mangoes for N2,450.00. She sold the pawpaw at a profit of 40% and the mangoes at a profit of 30%. If her profit on the entire transaction was N855.00, find the: (i) cost price of a basket of pawpaw; (ii) selling price of the 100 baskets of mangoes.
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(a) (−8 + 6d)/(−8 + 8d) = 5/8 → −64 + 48d = −40 + 40d → 8d = 24 → d = 3
(b) Let a basket of pawpaw cost x and a basket of mangoes cost y.
30x + 100y = 2450 … (1)
Profit: 0.4(30x) + 0.3(100y) = 855 → 12x + 30y = 855 … (2)
Solving: x = N40.00, y = N12.50
(i) Cost price of a basket of pawpaw = N40.00
(ii) Selling price of 100 baskets of mangoes = 1.3 × 100 × 12.50 = N1,625.00
Write one equation for the total cost and one for the total profit.