How do i solve this math problem?

Question

Tanya bought three adult tickets and one children's ticket to a movie for $21.70. Lee bought four adult tickets and four children's ticket for 39.60. Find the cost of one adult ticket and the cost of one children's ticket

Answer 1

You need to set up a system of equations. We have two different variables, the prices of the adult tickets and the price of the children's tickets. We know that 3 adult tickets plus 1 child's ticket cost 21.70 dollars. We can use A for the price of the adult tickets and C for the price of the children's tickets and create an expression we can work with.

3A+1C=21.70

Similarly, we can use these variables to express the cost of the tickets Lee bought.

4A+4C=39.60

Now we have two equations and two unknowns. There are a variety of ways to solve this but I will use the substitution method. In the first equation, I will subtract 3A from each side to get C by itself. Now we have an expression for the cost of the Children's tickets.

C=21.70-3A

I can then substitute this expression for the variable C in the second equation.

4A+4(21.70-3A)=39.60

4A+86.80-12A=39.60

47.20=8A

A=5.90 or in other words, 1 adult ticket costs $5.90.

Using this value for A, we can use it to calculate the cost of the children's tickets in the first equation.

C=21.70-3(5.90)

C=4 or a children's ticket costs $4.

Now the only thing we have left to do is check our work. If we use 5.9 for A and 4 for C in both equations, we should get 21.70 and 39.60 respectively.

3(5.9)+4=21.70

21.70=21.70 This check is good!

4(5.9)+4(4)=39.60

39.60=39.60 This check is good!

Since both checks were calculated to be the correct cost, we can say for certain that the cost of one adult ticket is $5.90 and the cost of one children's ticket is $4.00