Mr. RK Agrawal is owner of a famous amusement park in Delhi. Generally he does
not go to park and it is managed by team of staff. The ticket charge for the park is
Rs 150 for children and Rs 400 for adults.
One day Mr Agrawal decided to random check the park and went there. When he
checked the cash counter, he found that 480 tickets were sold and Rs 134500 was
collected.
(a) 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 the
problem?
(i) x + y = 480 and 3x + 8y = 2690 (ii) x + 2y = 480 and 3x + 4y = 2690
(iii) x + y = 480 and 3x + 4y = 2690 (iv) x + 2y = 480 and 3x + 8y = 2690
(b) How many children attended?
(i) 250 (ii) 500 (iii) 230 (iv) 460
(c) How many adults attended?
(i) 250 (ii) 500 (iii) 230 (iv) 460
(d) How much amount collected if 300 children and 350 adults attended?
(i) Rs 225400 (ii) Rs 154000 (iii) Rs 112500 (iv) Rs 185000
(e) One day total attended children and adults together is 750 and the total
amount collected is Rs 212500. What are the number of children and adults
attended?
(i) (700, 800) (ii) (350, 400) (iii) (800, 700) (iv) (400, 350)
Answers
Answer:
Step-by-step explanation:
(a) i
(b) iii
(c) i
(d) iv
(e) ii
(a) Given,
Price for children = 150 per child
Price for adult = 400 per adult
Total tickets sold = 480
Total amount collected = 1,34,500
To Find,
The correct system of equations that model the problem.
Solution (a),
Let the number of children that visited be x and the number of adults be y.
∴ x + y = 480 ......... (1)
⇒ 150x + 400y = 134500
⇒ 3x + 8y = 2690 (∴ Divided by 50) ..................(2)
Ans (a): (i) x + y = 480 and 3x + 8y = 2690
Solution (b) & (c),
Now subtract eq (2) from eq (1) to find the value of y,
3x + 8y = 2690
- x + y = 480
Now, Multiply eq (1) by 3 to equalize the value of x
3x + 8y = 2690
- 3x - 3y = - 1440
⇒5y = 1250
⇒ y = 1250/5
⇒ y = 250
Ans (c): (i) 250
Now, substitute y = 250 in eq (1)
x + 250 = 480
x = 230
Ans (b): (iii) 230
(d) Given,
Price for children = 150 per child
Price for adult = 400 per adult
To Find,
How much would have been collected if 300 children and 350 adults attended?
Solution (d),
Substitute this in 150x + 400y= ?
⇒ 150 (300) + 400 (350) = ?
⇒ 45,000 + 1,40,000= 1,85,000
Ans (d): (iv) 1,85,000
(e) Given,
Total attendance = 750
Total amount collected = Rs 2,12,500
To Find,
The number of children and adults that attended that day.
Solution (e),
According to the problem,
150x + 400y = 212500
⇒ 3x + 8y = 4250 (divided by 50) ........eq (3)
⇒ x + y = 750 ...........eq (4)
Now, multiply eq (4) by 3 to equalize, then subtract from eq (e)
3x + 8y = 4250
- 3x - 3y = - 2250
⇒ 5y = 2000
⇒y = 2000/5
⇒ y = 400
Now, substituting y = 400 in eq (4), we get,
x + 400 = 750
⇒ x = 350
∴ Ans(e): (ii) (350, 400); 400 adults and 350 children visited that day.
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