Adult tickets for a play cost $19 and child tickets cost $10. If there were 35 people at a performance and the theatre collected $476 from ticket sales, how many adults attended the play
Two equations, two unknowns.
A = adult tickets sold
C = child tickets sold
A + C = 35
19A + 10 C = 476
Solve
10A + 10C = 350
9A = 126
A = ?
To solve this problem, we can set up a system of equations based on the given information.
Let's assume "a" represents the number of adult tickets sold, and "c" represents the number of child tickets sold.
From the given information, we know that:
1. The cost of an adult ticket is $19, so the total revenue from adult ticket sales is 19a.
2. The cost of a child ticket is $10, so the total revenue from child ticket sales is 10c.
3. The total number of people who attended the performance is 35, which means a + c = 35.
4. The total revenue from ticket sales is $476, so 19a + 10c = 476.
Now, we have a system of two equations:
a + c = 35 (Equation 1)
19a + 10c = 476 (Equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve using the substitution method. From Equation 1, we can express "a" in terms of "c":
a = 35 - c
Now substitute this expression for "a" into Equation 2:
19(35 - c) + 10c = 476
Simplify:
665 - 19c + 10c = 476
-9c = 476 - 665
-9c = -189
Divide both sides by -9:
c = -189 / -9
c = 21
So, the number of children who attended the play is 21. Now, substitute this value back into Equation 1 to find the number of adults:
a + 21 = 35
a = 35 - 21
a = 14
Therefore, there were 14 adults who attended the play.