Theory question 106
Linear and Simultaneous Equations(a) Two positive whole numbers P and q are such that P is greater than q and their sum is equal to three times their difference. (i) Express P in terms of q. (ii) Hence, evaluate (P2 + q2)/Pq.
(b) A man sold 100 articles at 25 for ₦66.00 and made a gain of 32%. Calculate his gain or loss per cent if he sold them at 20 for ₦50.00.
Show the model answer
Model answer
(a)(i) P + q = 3(P − q) → 4q = 2P → P = 2q.
(ii) (4q2 + q2)/(2q × q) = 5q2/2q2 = 5/2.
(b) Selling price = 4 × 66 = ₦264 = 132% of the cost, so cost = ₦200.
New selling price = 5 × 50 = ₦250. Gain = ₦50 = 50/200 × 100% = 25% gain.
Explanation
Find the cost price first from the 32% gain.