admission to a park is $5 for an adult ticket and $1 for a child. If $100 was collected and 28 admissions were sold on a day, how many tickets were sold and how many child tickets were sold
To find out how many tickets were sold, we can start by setting up a system of equations based on the given information.
Let's assume the number of adult tickets sold is A, and the number of child tickets sold is C.
From the problem, we know two things:
1. The total money collected from selling adult tickets is $5 multiplied by the number of adult tickets sold, which is 5A.
2. The total money collected from selling child tickets is $1 multiplied by the number of child tickets sold, which is 1C.
We are also given the following information:
1. The total money collected is $100.
2. The total number of admissions sold, considering both adult and child tickets, is 28.
Now, we can set up the equations:
Equation 1: 5A + 1C = 100 (since the total money collected is $100)
Equation 2: A + C = 28 (since the total admissions sold is 28)
Now, let's solve the system of equations.
Multiply Equation 2 by 5:
5A + 5C = 140
Subtract Equation 1 from the above equation:
(5A + 5C) - (5A + 1C) = 140 - 100
4C = 40
Divide both sides of the equation by 4:
C = 10
Now, substitute the value of C into Equation 2:
A + 10 = 28
Subtract 10 from both sides of the equation:
A = 18
Therefore, 18 adult tickets and 10 child tickets were sold.