The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected.
How many children and how many adults attended?
(Note: Provide a detailed solution to help with understanding.)
Answer (3)
To solve this problem, you'll need to create a system of equations and then solve for the variables. For my two equations, x = # of children and y = # of adults
We know from the problem that the total amount of people who attended the fair is 2200, so that tells us that the number of children (x) plus the number of adults (y) will give us 2200. So, that's our first equation.
x + y = 2200
We also know that the total amount of money collected was $5050. This tells us that the number of children's tickets sold (1.50 * x) plus the number of adult's tickets sold (4 * y) will give us $5050. So, that's our second equation.
1.50x + 4y = 5050
Now, you take both equations and solve for the variables. x + y = 2200 1.50x + 4y = 5050
x + y = 2200 x = -y + 2200
1.50(-y + 2200) + 4y = 5050 -1.50y + 3300 +4y = 5050 3300 + 2.5y = 5050 2.5y = 1750 y = 700
Now that you know that y =700, you plug that information into either of the two equations and solve for x. I'm going to use the first equation because it's easier. x + y = 2200 x + 700 = 2200 x = 1500
So, x = 1500 and y = 700
There were 1500 children and 700 adults in attendance.
Let's define two variables:
c for the number of children
a for the number of adults
We have the following two equations based on the problem statement:
Total people: c + a = 2200
Total money collected: 1.50c + 4a = 5050
From the first equation, solve for one variable in terms of the other: c = 2200 - a
Substitute this expression into the second equation: 1.50(2200 - a) + 4a = 5050
Simplify and solve for a:
3300 - 1.50a + 4a = 5050
2.50a = 1750
a = 700 (number of adults)
Substitute a back into the first equation to find c: c = 2200 - 700 = 1500 (number of children)
Therefore, the number of children who attended the fair is 1500 and the number of adults is 700.
To find the number of children and adults at the fair, we created two equations based on the total count of 2200 attendees and the total amount collected of $5050. Solving these equations, we found there were 1500 children and 700 adults attending the fair.
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