Can someone help me find the answer?

Question

Arianna and Samantha go to the movie theater and purchase refreshments for their

frier ds.

Arianna spends a total of $118.75 on 10 drinks and 5 bags of popcorn.

Samantha spends a total of $157.75 on 9 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 drink, to the nearest cent.

Answer 1

Hi Armani,

Let's use the variable d to represent the cost of one drink and the variable p represent the cost of one popcorn.

Now we can write two equations based on the info given in the problem:

10d + 5p = $118.75

9d + 10p = $157.75

These equations can be solved using elimination. Multiply the first equation by -2:

10d + 5p = 118.75 becomes -20d - 10p = -237.50

9d + 10p = 157.75

Now combine the two equations to find the value of d:

-20d - 10p = -237.50

9d + 10p = 157.75

-11d = -79.75

-11d/-11 = -79.75/ -11

d= 7.25

The cost of one drink is $7.25

You can also use either equation to find the value of p. Using the second equation, substitute 7.25 for d:

9d + 10p = 15775

9• 7.25 + 10•p = 157.75

65.25 + 10p = 157.75

65.25 + 10p - 65.25 = 157.75 - 65.25

10p = 92.50

10p/ 10 = 92.50/ 10

p = 9.25

The cost of one popcorn is $9.25

Hope this helps you Armani. Send a message is you need any lessons!