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.
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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 child pass is "x" (in Rs).
According to the given information, the rate of adult passes is Rs.20 more than the children pass. Therefore, the price of an adult pass would be "x + 20" (in Rs).
Now, let's use this information to set up the equations:
Equation 1: Number of adult passes * Price of an adult pass = Total amount collected from adult passes
Equation 2: Number of children passes * Price of a child pass = Total amount collected from children passes
According to the problem, 50 adult passes and 200 children passes were sold, and the total amount collected was Rs.2250.
Let's substitute the values into the equations:
Equation 1: 50 * (x + 20) = Total amount collected from adult passes
Equation 2: 200 * x = Total amount collected from children passes
Now, we can rewrite the equations:
50x + 1000 = Total amount collected from adult passes
200x = Total amount collected from children passes
Since the total amount collected from adult passes plus the total amount collected from children passes equals Rs.2250, we can form another equation:
Total amount collected from adult passes + Total amount collected from children passes = 2250
50x + 1000 + 200x = 2250
Combine like terms:
250x + 1000 = 2250
Subtract 1000 from both sides:
250x = 1250
Divide both sides by 250:
x = 5
So, the price of a child pass is Rs.5.
To find the price of an adult pass, we can substitute this value back into the equation:
Price of an adult pass = x + 20 = 5 + 20 = Rs.25
Therefore, the price of an adult pass is Rs.25.