The price of commodities X, Y and Z are respectively x, y and z rupees per unit. Mr. A purchases 3 units of Z and sells of 2 units of X and 4 units of Y. Mr. B purchases 5 units of Y and sells of 3units of X and 2 unit of Z. Mr C purchases 1 unit of X and sells of 3 units of Y and 2 units of Z. In this process A, B and C earn Rs. 12, 13 and 17 respectively. Find the price per unit of the three commodities.
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Step-by-step explanation:
commodity sold is income and commodity purchased is expenditure. earning = income - expenditure. forming equations from given information, we have
2x+4y-3z = 12............(1)
3x-5y+2z = 13............(2)
-x+3y+2z.= 17.............(3)
(3)*2 + (1)
= 10y + z = 46............(4)
(3)*3 + (2)
4y + 8z = 64
or y + 2z = 16.............(5)
(4)*2-(5)
19y = 76
y = 4
from (5)
2z = 16-4 = 12
z = 6
from (3)
x = 3y+2z-17
= 12+12-17
= 24-17
x= 7
hence prices are
x= 7, y = 4 and z= 6
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