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Linear Equation In Two Varialbles: Miscellaneous Problem
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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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