Question

Alex and Brandon bought candy and popcorn at the movie theater. Alex bought 2 tubs of popcorn

and 3 boxes of candy for $19.50. Brandon bought 2 tubs of popcorn and 5 boxes of candy for
$22.50. If all the popcorn costs the same and all the candy costs the same, how much did one tub of
popcorn cost?

Answer 1

By creating a system of equations from the given purchases and using the elimination method, we determine the cost of one tub of popcorn to be $7.50.

Step-by-step explanation:

To find out the cost of one tub of popcorn, we can set up a system of equations based on the information given:

• Alex's purchase: 2p + 3c = 19.50
• Brandon's purchase: 2p + 5c = 22.50

We can solve this system of equations using either the substitution or elimination method. Let's use the elimination method to find the value of 'p' which represents the cost of one tub of popcorn:

1. First, we will multiply the first equation by -1 to help eliminate the 'p' variable:
2. -2p - 3c = -19.50
3. Add the resulting equation to the second equation:
4. (-2p - 3c) + (2p + 5c) = (-19.50) + 22.50
5. -2p and 2p cancel out. Now we have:
6. 2c = 3.00
7. Divide both sides by 2:
8. c = 1.50
9. Now use the value of c to solve for p in one of the original equations. Let's use the first equation:
10. 2p + 3(1.50) = 19.50
11. Which simplifies to:
12. 2p + 4.50 = 19.50
13. Subtract 4.50 from both sides:
14. 2p = 15.00
15. Divide both sides by 2 to find the cost of one tub of popcorn:
16. p = 7.50

Therefore, one tub of popcorn costs $7.50.