Adults 5.00
Kids 3:50
240 tickets sold for 1140
How many adults? How many kids?
a + k = 240
5a + 3.5k = 1140
solve them
To determine the number of adults and kids, we can set up a system of equations based on the given information.
Let's assume that "x" represents the number of adults, and "y" represents the number of kids. From the information given, we can establish two equations:
Equation 1: Adults: 5.00x
Equation 2: Kids: 3.50y
We also know that a total of 240 tickets were sold for $1140. This information can be represented by the following equation:
Equation 3: 5.00x + 3.50y = 1140
Now, we can solve this system of equations to find the values of "x" and "y."
To do this, we can use the method of substitution or elimination. Let's use elimination:
Multiply Equation 1 by 100 to eliminate decimals:
500x
Multiply Equation 2 by 200 to eliminate decimals:
700y
Now, we have:
500x + 700y = 114000 (Equation 4)
We can use Equation 4 and Equation 3 to solve for "x" and "y" simultaneously.
5.00x + 3.50y = 1140 (Equation 3)
500x + 700y = 114000 (Equation 4)
Multiply Equation 3 by 200 to eliminate decimals:
1000x + 700y = 228000 (Equation 5)
Now, subtract Equation 4 from Equation 5:
(1000x + 700y) - (500x + 700y) = 228000 - 114000
This simplifies to:
500x = 114000
To solve for "x," divide both sides of the equation by 500:
x = 114000 / 500
x = 228
Therefore, the number of adults, "x," is 228.
Now, substitute this value of "x" into Equation 3 to find the number of kids, "y":
5.00(228) + 3.50y = 1140
Multiply:
1140 + 3.50y = 1140
Subtract 1140 from both sides:
3.50y = 0
Divide both sides by 3.50:
y = 0
Therefore, the number of kids, "y," is 0.
In conclusion, there are 228 adults and 0 kids, based on the given information.