Linear Equation In Two Varialbles: Miscellaneous Problem

 Linear Equation In Two Varialbles: Miscellaneous Problem Example: A man sold a chair and a table together for \$ 152 thereby making a profit of 25% on the chair and 10% on table, By selling them together for \$ 153.5 he would have made a profit of 10% on the chair and 25% on the table. Find the cost price of each.
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 Solution: Let the cost price of one chair be \$ x and that of one table be \$ y. Profit on a chair = 25% Selling price ot one chair = x + (25/100)x = (125/100)x Profit on a table = 10% Selling Price of 1 table = y + (10y/100) = 110/100y According to the given condition, you have (125/100)x + (110/100)y = 152 125 x + 110 y= 15200 25 x + 22 y = 3040 ...(i) If profit on a chair is 10% and on a table is 25%, then total selling price is \$ 153.5 (x + (10/100)x) + (y + (25/100)y) = 153.5 (110/100)x + (125/100)y = 153.5 110 x + 125 y = 15350 22 x + 25 y = 3070 ...(ii) Subtracting equation (ii) from equation (i), you get 3x - 3y = - 30 x - y = -10   ...(iii) Adding equations (ii) and (i), you get 47x + 47y = 6110 x + y = 130 ...(iv) Solving equations (iii) and (iv), you get x = 60 and y = 70. Hence, the cost price of a chair is \$ 60 and that of a table is \$ 70.

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