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.