Theory question 106
Linear and Simultaneous Equations(a) If 3/(2p − ½) = (⅓)/(¼p + 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.
Show the model answer
Model answer
(a) Cross-multiply: 3(¼p + 1) = ⅓(2p − ½) → ¾p + 3 = ⅔p − ⅙ → (1/12)p = −19/6 → p = −38.
(b) Cost price = 760 × 100/120 ≈ GH¢633.33. Selling price = 95% of 760 = GH¢722.
Profit = 722 − 633.33 = GH¢88.67. Percentage profit = 88.67/633.33 × 100% ≈ 14%.
Explanation
Find the cost price from the marked price first.