Final answer:
To solve for the number of child tickets sold, we create a system of equations from the given information and solve it to find that 31 child tickets were sold at the movie theater on Friday.
Step-by-step explanation:
Solving a System of EquationsTo find out how many child tickets were sold at the movie theater, we can set up a system of equations. Let x be the number of child tickets and y be the number of adult tickets sold. From the problem, we know that adult tickets are three times the number of child tickets (y = 3x) and that the total sales were $979.60. Using the prices given for child tickets ($5.50) and adult tickets ($8.70), we can write the following equation.
- 5.50x + 8.70y = 979.60 (Total sales)
- y = 3x (Three times as many adult tickets as child tickets)
Substituting the second equation into the first gives us:
5.50x + 8.70(3x) = 979.60
Which simplifies to:
31.60x = 979.60
Solving for x gives us:
x = 979.60 / 31.60
x = 31
Therefore, 31 child tickets were sold that day.