**Q) Essel World is one of India’s largest amusement parks that offers a diverse range of thrilling rides, water attractions and entertainment options for visitors of all ages. The park is known for its iconic ‘‘Water Kingdom’’ section, making it a popular destination for family outings and fun-filled adventure. ****The ticket charges for the park are Rs. 150 per child and Rs. 250 per adult.**

**On a day, the cashier of the park found that 300 tickets were sold and an amount of Rs. 55,000 was collected.**

**Based on the above, answer the following questions : **

**(i) If the number of children visited be x and the number of adults visited be y, then write the given situation algebraically. **

**(ii) How many children visited the amusement park that day? **

**(iii) How many adults visited the amusement park that day? **

**(iv) How much amount will be collected if 250 children and 100 adults visit the amusement park? **

**Ans: **

**(i) algebraic expressions for the situations:**

**Situation 1:**

No. of Children visited = x

and No. of adults visited = y

Also it is given that total 300 tickets were sold.

∴ No. children’s tickets sold + No. children’s tickets sold = total no. of tickets sold

**∴ x + y = 300 ….. (i)**

**Situation 2:**

Child ticket cost = Rs. 150 and No. of Children visited = x

∴ Amount collected by children’s tickets sale = No. of children x Cost of one child ticket = 150 x

Similarly, Adult ticket cost = Rs. 250 and No. of adults visited = y

∴ Amount collected by adults’ tickets sale = No. of adults x Cost of one adult ticket = 250 y

∴ Total Amount collected by all tickets sale = Amount collected by children’s tickets sale + Amount collected by adults’ tickets sale

∴ Total Amount = 150 x + 250 y

Given that Amount collected is Rs. 55,000

∴ 150 x + 250 y = 55,000

**∴ 3 x + 5 y = 1100 ……… (ii)**

**(ii) Number of children visited the amusement park:**

To solve for values of x & y, we multiply equation (i) by 5 and subtract equation (i) from it:

5 (x + y) – (3 x + 5 y) = 5 (300) – 1100

5 x + 5 y – 3 x – 5 y = 1500 – 1100

2 x = 400

x =

**x = 200**

**Therefore, 200 children visited the amusement park.**

**(iii) Number of adults visited the amusement park:**

By substituting this value of x in equation (i), we get:

x + y = 300

200 + y = 300

y = 300 – 200

**y = 100**

**Therefore, 100 adults visited the amusement park.**

(iv) Amount collected by visit of 250 children and 100 adults:

New value of x (number of children visited) = 250

Cost of one child ticket = 150

∴ Amount collected by children’s tickets sale = No. of children x Cost of one child ticket = 250 x 150 **= Rs. 37,500**

New value of y (number of adults visited) = 100

Similarly, Adult ticket cost = Rs. 250

∴ Amount collected by adults’ tickets sale = No. of adults x Cost of one adult ticket = 100 x 250** = Rs. 25,000**

∴ Total Amount collected by all tickets sale = Amount collected by children’s tickets sale + Amount collected by adults’ tickets sale

∴ Total Amount = 37,500 + 25,000 = **Rs. 62,500**

**Therefore, Rs. 62,500 collected by visit of 250 children and 100 adults:**

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