i really need help

Question

Sydney and Mila go to the movie theater and purchase refreshments for their friends.

Sydney spends a total of $28.50 on 9 drinks and 2 bags of popcorn.

Mila spends a total of $42.50 on 5 drinks and 10 bags of popcorn.

Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn.

Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.

Answer 1

Let d = the price of 1 drink

and p = the price of 1 bag of popcorn.

Based on the word problem we can create the following equations:

9d + 2p = 28.50

5d + 10p = 42.50

Now that we've created the equations, we can use the Elimination method to solve for p, the price of one bag of popcorn. We'll multiply the first equation by 5 and the second equation by 9 in order to eliminate d:

5 [9d + 2p = 28.50] ---> 45d + 10p = 142.50

9 [5d + 10p = 42.50] ---> 45d + 90p = 382.50

Since both equations now have a 45d, we can subtract each term in the second equation from each term in the first equation:

45d + 10p = 142.50

-(45d + 90p = 382.50)

_____________________

0d + (-80p) = -240

Finally we can solve for p by dividing both sides by -80:

-80p = -240

p = 3

The cost of one bag of popcorn is $3.

*Note: We can also now find the cost of one drink by substituting 3 in for p in one of our two equation and solve for d, but the original question only asks for the price of popcorn.

Answer 2

Let d = the number of drinks purchased, and p = the number of bags of popcorn bought. The two equations are:

9d + 2p = 28.50

5d + 10p = 42.50

You can now use either the Elimination or Substitution Method to solve this linear system.