A village has a population of 500 and a play is performed in that vill

1.	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» Answer: From the condition, you have these TWO EQUATIONS x + y + z = 500 (1) 748x + 712y + 45z = 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 748x + 712y + 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 = %28275000-703x%29%2F667, 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.

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»

Answer:

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 = %28275000-703x%29%2F667, 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.