Jake is buying a movie ticket and box of popcorn for $12. The ticket costs 2 times as much as the popcorn. How much does the popcorn cost? How much does the ticket cost?

t+p = 12

t = 2p
now crank it out

Let's say the cost of the popcorn is "x" dollars.

According to the given information, the ticket costs 2 times as much as the popcorn, so the ticket costs 2*x dollars.
The total cost of the movie ticket and popcorn is $12, so we can write the equation:
x + 2*x = 12
Combining like terms, we get:
3*x = 12
Dividing both sides by 3, we find:
x = 4
So, the popcorn costs $4.
Since the ticket costs 2 times as much as the popcorn, the ticket costs 2*4 = $8.

To find the cost of the popcorn and the ticket, we can set up a system of equations. Let's denote the cost of the popcorn as "P" and the cost of the ticket as "T."

According to the given information, the ticket costs 2 times as much as the popcorn. Therefore, we can write the equation:

T = 2P

We also know that Jake is buying a movie ticket and box of popcorn for a total of $12. So, we can write another equation:

T + P = 12

Now, we can solve this system of equations to find the values of P (popcorn cost) and T (ticket cost).

Substituting T = 2P into the second equation, we get:

2P + P = 12

Combining like terms, we have:

3P = 12

Dividing both sides by 3, we find:

P = 4

So, the cost of the popcorn is $4.

To find the cost of the ticket, we substitute the value of P back into one of the equations. Let's use T = 2P:

T = 2(4) = 8

Therefore, the ticket costs $8.