in a cinema hall 300 tickets were sold. the total sales of tickets was rs 12500. if the tickets were two denominations of rs 25 and rs 50. how many of each were sold?
To solve this problem, we can use a system of equations. Let's assume that the number of tickets sold at Rs 25 is represented by 'x', and the number of tickets sold at Rs 50 is represented by 'y'.
Given that a total of 300 tickets were sold, we can write the equation:
x + y = 300 Equation 1
The total sales of tickets was Rs 12,500, so we can write another equation based on the value of each ticket:
25x + 50y = 12,500 Equation 2
Now, we have a system of two equations with two variables. We can solve this system to find the values of 'x' and 'y'.
One way to solve it is by using the substitution method:
1. Rearrange Equation 1 to express 'x' in terms of 'y':
x = 300 - y
2. Substitute the value of 'x' in Equation 2:
25(300 - y) + 50y = 12,500
3. Simplify the equation:
7,500 - 25y + 50y = 12,500
25y = 12,500 - 7,500
25y = 5,000
4. Solve for 'y':
y = 5,000 / 25
y = 200
5. Substitute the value of 'y' back into Equation 1 to find 'x':
x + 200 = 300
x = 300 - 200
x = 100
Therefore, 100 tickets were sold at Rs 25 each, and 200 tickets were sold at Rs 50 each.
call the tickets H or Low.
H+L=300
25L+50H=12500
solve for H, and L