(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 (frac{p^{2} + q^{2}}{pq}).
(b) A man sold 100 articles at 25 for N66.00 and made a gain of 32%. Calculate his gain or loss percent if he sold them at 20 for N50.00.
Explanation
(a)(i) (p > q …. (1))
(p + q = 3(p – q) …… (2))
From (2), (p + q = 3p – 3q)
(p – 3p = – 3q – q implies – 2p = – 4q)
(p = 2q)
(ii) (frac{p^{2} + q^{2}}{pq})
= (frac{(2q)^{2} + q^{2}}{2q times q})
(frac{4q^{2} + q^{2}}{2q^{2}})
= (frac{5q^{2}}{2q^{2}})
= (frac{5}{2})
(b) Selling price = (frac{100 times 66}{25})
= (N264.00)
Using (frac{SP – CP}{CP} = % gain)
(frac{264 – CP}{CP} = frac{32}{100})
(100(264 – CP) = 32CP)
(26400 = 32CP + 100CP = 132CP)
(CP = frac{26400}{132})
= (N200)
When he sells 20 for N50, Selling price = (frac{100 times 50}{20} = N250.00)
Hence, he made gain.
(% gain = frac{250 – 200}{200} times 100%)
(frac{1}{4} times 100%)
= (25% gain)