At the city museum, child admission $5.30 is and adult admission is $9.00. On Friday, three times as many adult tickets as child tickets were sold, for a total sales of $872.10. How many child tickets were sold that day?
children tickets ---- x
adult tickets ------- 3x
9x + 5.3(3x) = 872.10
take over from here
To solve this problem, we will use a system of equations. Let's assume the number of child tickets sold is "x", and the number of adult tickets sold is "y".
From the given information, we can establish two equations:
1) The total sales from child tickets: 5.30x
2) The total sales from adult tickets: 9.00y
According to the problem, three times as many adult tickets as child tickets were sold, so we can also say:
3) y = 3x
Furthermore, we know that the total sales from both types of tickets was $872.10, so we can write the equation:
4) 5.30x + 9.00y = 872.10
Now, we have a system of equations with three equations (equations 1, 3, and 4) and three variables (x, y, and y). We can solve this system of equations to find the value of x (the number of child tickets sold).
First, let's substitute equation 3 (y = 3x) into equation 4:
5.30x + 9.00(3x) = 872.10
5.30x + 27x = 872.10
32.30x = 872.10
Next, we solve for x by dividing both sides of the equation by 32.30:
x = 872.10 / 32.30
x ≈ 27
Therefore, approximately 27 child tickets were sold that day at the city museum.