Answer:
81 adult tickets were sold that day
Explanation:
We will need a system of equations to solve for the number of adult tickets sold.
First equation: For reference, revenue refers to price * quantity.
- We know that the revenue earned from the child tickets plus the revenue earned from the adult tickets equals the total revenue ($956.60):
(price of child tickets * quantity of child tickets) + (price of adult tickets * quantity of adult tickets) = total revenue.
Allowing C to represent the number of child tickets and A to represent the number of adult tickets, our first equation is:
5.20C + 8.60A = 956.60
Second Equation:
- We further know that the quantity of child tickets plus the quantity of adult tickets equals the total quantity of tickets sold (131)
Thus, our second equation is:
C + A = 131
Method to Solve: We can solve for A using substitution. Let's isolate C in the second equation and plug it in for C in the first equation:
Isolating C in second equation:
(C + A = 131) - A
C = -A + 131
Substituting -A + 131 for C in first equation:
5.20 (-A + 131) + 8.60A = 956.60
-5.20A + 681.20 + 8.60A = 956.60
3.40A + 681.20 = 956.60
3.40A = 275.40
A = 81
Optional Checking Step:
We can check that we've correctly found the correct number of adult tickets sold by first using the second equation in our system to solve for C:
C + 81 = 131
C = 50
Second, we want to plug in 81 for A and 50 for C in both equations in our system and check that we get 956.60 and 131 respectively:
Checking solutions for first equation:
5.20(50) + 8.60(81) = 956.60
260.00 + 696.60 = 956.60
956.60 = 956.60
Checking solutions for second equation:
50 + 81 = 131
131 = 131