Answer: The price for one adult ticket is $10 and the price for one child ticket is $7.
Step-by-step explanation:
The correct exercise is: "At a movie theater, the price of 2 adult tickets and 4 children tickets is 48$. The price of 5 adult tickets and 2 child tickets is 64$. What is the price for one adult and one child?"
Let be "a" the price (in dollars) for one adult ticket and "c" the price (in dollars) for one child ticket.
Set up a System of equations with the data given in the exercise:
[tex]\left \{ {{2a+4c=48} \atop {5a+2c=64}} \right.[/tex]
You can use the Elimination method to solve the System of equations:
1. Multiply the second equation by -2.
2. Add the equations.
3. Solve for "a".
Then:
[tex]\left \{ {{2a+4c=48} \atop {-10a-4c=-128}} \right.\\........................\\-8a=-80\\\\a=\frac{-80}{-8}\\\\a=10[/tex]
4. Substitute the value of "a" into any original equation.
5. Solve for "c":
[tex]2(10)+4c=48\\\\4c=48-20\\\\c=\frac{28}{4}\\\\c=7[/tex]
