The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 292 people entered the park, and the admission fees collected totaled 838.00 dollars. How many children and how many adults were admitted?
c+a = 292
1.50c + 4.00a = 838.00
Now just solve for c and a.
To solve this problem, let's use a system of equations.
Let's assume the number of children admitted to the amusement park is represented by 'c' and the number of adults admitted is represented by 'a.'
According to the information given, we have two equations:
Equation 1: c + a = 292 (The total number of people admitted is 292)
Equation 2: 1.50c + 4a = 838 (The total admission fees collected is $838)
Now, we can solve this system of equations to find the values of 'c' and 'a.'
First, let's solve Equation 1 for 'c':
c = 292 - a
Next, substitute this value of 'c' into Equation 2:
1.50(292 - a) + 4a = 838
Now, simplify and solve for 'a':
438 - 1.50a + 4a = 838
2.50a = 400
a = 400 / 2.50
a = 160
Now, substitute the value of 'a' back into Equation 1 to find 'c':
c + 160 = 292
c = 292 - 160
c = 132
Therefore, the number of children admitted (c) is 132, and the number of adults admitted (a) is 160.