Question 1144331: A village has a population of 500 and a play is performed in that village. Men play - 748 rupees, women - 712 rupees and children - 45 rupees to watch the play. The theater company receives a total of Rs. 300,000 (3 lakhs). So what will be the number of men, women and children in that village?
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
From the condition, you have these two equations
x + y + z = 500 (1)
748*x + 712*y + 45*z = 300000 (2)
where x is the number of men, y is the number of women and z is the number of children.
From equation (1), express z = 500-x-y and substitute it into equation (2). You will get
748*x + 712*y + 45*(500-x-y) = 300000.
Simplify it
703x + 667y = 300000 - 45*500 = 277500.
Now we should find integer solution/solutions to the last equation.
The simplest way is to express y =  , put this formula into Excel, run for x= 1, 2, 3, 4, . . . and search for integer y
In this way I got the integer solution x = 149, y = 259.
Then z = 500-x-y = 500-149-259 = 92.
ANSWER. 149 men, 259 women and 92 children.
Solved.
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