3. Mr. RK Agrawal is owner of a famous amusement park in Delhi. Generally he doesnot go to park and it is managed by team of staff. The ticket charge for the park is Rs150 for children and Rs 400 for adults. One day Mr Agrawal decided to random checkthe park and went there. When he checked the cash counter, he found that 480 ticketswere sold and Rs 134500 was collected.(i) Let the number of children visited be x and the number of adults visited be y .Which of the following is the correct system of equation that model theproblem ?(ii) How many children attended?(iii) How many adults attended?(iv) How much amount collected if 300 children and 350 adults attended?(v) One day total attended children and adults together is 750 and the total amountcollected is Rs 212500. What are the number of children and adults attended ?
Question
- Mr. RK Agrawal is owner of a famous amusement park in Delhi. Generally he doesnot go to park and it is managed by team of staff. The ticket charge for the park is Rs150 for children and Rs 400 for adults. One day Mr Agrawal decided to random checkthe park and went there. When he checked the cash counter, he found that 480 ticketswere sold and Rs 134500 was collected.(i) Let the number of children visited be x and the number of adults visited be y .Which of the following is the correct system of equation that model theproblem ?(ii) How many children attended?(iii) How many adults attended?(iv) How much amount collected if 300 children and 350 adults attended?(v) One day total attended children and adults together is 750 and the total amountcollected is Rs 212500. What are the number of children and adults attended ?
Solution
(i) Let the number of children visited be x and the number of adults visited be y.
The correct system of equations that models the problem is: x + y = 480 (equation 1) - This equation represents the total number of tickets sold, which is 480. 150x + 400y = 134500 (equation 2) - This equation represents the total amount collected, which is Rs 134500.
(ii) To find the number of children attended, we need to solve the system of equations. We can use substitution or elimination method. Let's use the elimination method.
From equation 1, we can express x in terms of y: x = 480 - y
Substituting this value of x in equation 2, we get: 150(480 - y) + 400y = 134500 72000 - 150y + 400y = 134500 250y = 62500 y = 250
So, the number of adults attended is 250.
(iii) To find the number of children attended, we can substitute the value of y in equation 1: x + 250 = 480 x = 480 - 250 x = 230
So, the number of children attended is 230.
(iv) To find the amount collected if 300 children and 350 adults attended, we can substitute these values in equation 2: 150(300) + 400(350) = 134500 45000 + 140000 = 134500 185000 = 134500
So, the amount collected if 300 children and 350 adults attended is Rs 185000.
(v) To find the number of children and adults attended when the total attended is 750 and the total amount collected is Rs 212500, we can solve the system of equations.
Using the same equations as before: x + y = 480 (equation 1) 150x + 400y = 212500 (equation 2)
Substituting the value of x from equation 1 in equation 2, we get: 150(480 - y) + 400y = 212500 72000 - 150y + 400y = 212500 250y = 140500 y = 562
So, the number of adults attended is 562.
Substituting this value of y in equation 1, we get: x + 562 = 480 x = 480 - 562 x = -82
Since the number of attendees cannot be negative, there seems to be an error in the given information or calculations.
Please double-check the given information or calculations to find the correct number of children and adults attended.
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