Movie tickets for an adult and 3 children cost $20 dollars. An adult ticket costs $2 more than a child's ticket. What is the cost of an adult ticket ?

Question

Movie tickets for an adult and 3 children cost $20 dollars. An adult ticket costs $2 more than a child's ticket. What is the cost of an adult ticket ?I have tried helplessly and don't quite get it.

Answer 1

So we're looking for the cost of an adult ticket, so let say an adult ticket costs X dollars.

We can then assign another variable to the amount a child's ticket costs, lets say a child's ticket costs Y dollars

And we know an adults tickets are 2 dollars more than the child's ticket. Thus,

X = Y + 2

And the total for 3 child's tickets and one adult ticket is 20 dollars. Thus,

X + 3Y = 20

plugging in our equation relating the price of an adult and child ticket and solving for the price of a child's ticket we have,

(Y + 2) + 3Y = 20

4Y + 2 = 20

4Y = 18

Y = 4.5

Then plugging Y back into the equation for X, we find our answer of the price for an adult ticket,

X = Y + 2

X = 4.5 + 2

X = 6.5

We can check this answer by adding up the tickets purchased,

X + 3Y =

6.5 + 3(4.5) = 20 yay