Questions: Participation Activity #6 This is similar to Try It #8 in the OpenStax text. Meal tickets at the circus cost 4.00 for children and 12.00 for adults. If 1,850 meal tickets were bought for a total of 15,800, how many children and how many adults bought meal tickets? Enter the exact answers. The number of adult meal tickets sold was Number . The number of child meal tickets sold was Number .

Solution Steps

To solve this problem, we need to set up a system of linear equations based on the information given. Let \( c \) represent the number of children's tickets and \( a \) represent the number of adult tickets. We have two equations: one for the total number of tickets and one for the total cost. The equations are:

1. \( c + a = 1850 \) (total tickets)
2. \( 4c + 12a = 15800 \) (total cost)

We can solve this system of equations using substitution or elimination to find the values of \( c \) and \( a \).

We define \( c \) as the number of children's meal tickets and \( a \) as the number of adult meal tickets. Based on the problem, we can set up the following system of equations:

1. \( c + a = 1850 \)
2. \( 4c + 12a = 15800 \)

We solve the system of equations to find the values of \( c \) and \( a \). From the first equation, we can express \( a \) in terms of \( c \): \[ a = 1850 - c \] Substituting this expression into the second equation gives: \[ 4c + 12(1850 - c) = 15800 \] Simplifying this leads to: \[ 4c + 22200 - 12c = 15800 \] \[ -8c + 22200 = 15800 \] \[ -8c = 15800 - 22200 \] \[ -8c = -6400 \] \[ c = 800 \]

Substituting \( c = 800 \) back into the equation for \( a \): \[ a = 1850 - 800 = 1050 \]

Final Answer