Question:
The admission fee at a carnival is $3.00 for children and $5.00 for adults. On the first day 1,500 people enter the fair and $5740 is collected. How many children and how many adults attended the carnival?
Answer:
Number of children and adults attended the carnival are 880 and 620 respectively
Explanation:
Given:
The admission fee at a carnival for children = $3.00
The admission fee at a carnival for adults = $5.00
Number of people entered the fare on first day= 1500
Total amount collected on the first day = $5740
To Find:
Number of children and adults attended the carnival =?
Solution:
Let
The number of children be x
The number of adults be y
The we know that on the first day the total number children visited the fare was 1500
x + y = 1500
x = 1500 - y------------------------------(1)
Also the total fare collected was $5740
x(3) + y(5) = 5740
3x + 5y = 5740-------------------(2)
Substituting (1) in (2),
3 (1500 - y) + 5y = 5740
4500 -3y + 5y = 5740
-3y + 5y = 5740 - 4500
2y = 1240
y = 620 adults
From 1 ,
x = 1500 - 620
x =880