(a) If (frac{3}{2p – frac{1}{2}} = frac{frac{1}{3}}{frac{1}{4}p + 1}), find p.
(b) A television set was marked for sale at GH¢ 760.00 in order to make a profit of 20%. The television set was actually sold at a discount of 5%. Calculate, correct to 2 significant figures, the actual percentage profit.
Explanation
(a) (frac{3}{2p – frac{1}{2}} = frac{frac{1}{3}}{frac{1}{4}p + 1})
(implies 3(frac{1}{4}p + 1) = frac{1}{3}(2p – frac{1}{2}))
(frac{3}{4}p + 3 = frac{2}{3}p – frac{1}{6})
(frac{3}{4}p – frac{2}{3}p = – 3 – frac{1}{6})
(frac{1}{12}p = – 3frac{1}{6})
(p = frac{-19}{6} div frac{1}{12})
(p = frac{-19}{6} times 12 = -38)
(b) (5% times ¢760.00 = frac{5}{100} times ¢760 = ¢38.00)
So the TV set was actually sold for ¢(760 – 38) = ¢722.00
Using,
(% profit = frac{text{SP – CP}}{CP} times 100%)
(20% = frac{760 – x}{x} times 100%)
(20% x = (760 – x) times 100%)
(x = 5(760 – x) implies x = 3800 – 5x)
(6x = 3800 implies x = ¢633.33)
Thus, the actual profit = actual SP – CP
= ¢(722 – 633.33)
= ¢88.67
Hence, actual %age profit = (frac{88.67}{633.33} times 100%)
= 14.0006%
= 14% (2 sig. figs)