for a charity show the rate of adult passes Rs.20 more than the children pass.when a company sold 50 adult and 200 children passes,the amount collected is Rs.2250.find the price of an adult pass.
a = c+20
50a + 200c = 2250
a = 25
Let's assume the cost of a children pass is x Rs.
According to the given information, the cost of an adult pass is Rs.20 more than the cost of a children pass.
So, the cost of an adult pass is (x + 20) Rs.
Now, let's calculate the total amount collected by selling 50 adult passes and 200 children passes.
The amount collected from selling adult passes = (50 * (x + 20)) Rs.
The amount collected from selling children passes = (200 * x) Rs.
Given that the total amount collected is Rs.2250:
(50 * (x + 20)) + (200 * x) = 2250
Simplifying the equation, we get:
50x + 1000 + 200x = 2250
250x + 1000 = 2250
250x = 2250 - 1000
250x = 1250
Dividing both sides of the equation by 250, we find:
x = 1250/250
x = 5
Therefore, the cost of a children pass is Rs.5.
As the cost of an adult pass is Rs.20 more than the cost of a children pass, we calculate:
Cost of an adult pass = 5 + 20
Cost of an adult pass = 25
So, the price of an adult pass is Rs.25.
To find the price of an adult pass, we can set up a system of equations based on the given information.
Let's assume that the price of a children pass is "x" (in Rs.). According to the question, the rate of an adult pass is Rs.20 more than the children pass.
Therefore, the price of an adult pass can be calculated as "x + 20" (in Rs.).
Now, we can use the given information that the company sold 50 adult passes and 200 children passes, and the total amount collected was Rs.2250.
The total amount collected from adult passes can be calculated as 50 times the price of an adult pass, which is:
50 * (x + 20)
The total amount collected from children passes can be calculated as 200 times the price of a children pass, which is:
200 * x
According to the question, the total amount collected from both passes is Rs.2250. So, we can set up the equation:
50 * (x + 20) + 200 * x = 2250
Now, we can solve this equation to find the value of "x" (the price of a children pass), and then calculate the price of an adult pass (x + 20).
50 * (x + 20) + 200 * x = 2250
Expanding the brackets:
50x + 1000 + 200x = 2250
Combining like terms:
250x + 1000 = 2250
Subtracting 1000 from both sides:
250x = 1250
Dividing both sides by 250:
x = 5
Now we know that the price of a children pass is Rs.5.
To find the price of an adult pass, we can substitute the value of "x" (5) into "x + 20":
5 + 20 = 25
So, the price of an adult pass is Rs.25.