systems of equations

Question

ophie and Elizabeth go to the movie theater and purchase refreshments for their friends.

Sophie spends a total of $72.50 on 5 drinks and 5 bags of popcorn.

Elizabeth spends a total of $163.50 on 15 drinks and 3 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

5d + 5p = 72.5

15d + 3p = 163.5

 

We can multiply the first equation by -3 to make -15d so the d's will cancel out.

 

-15d - 15p = -217.5

15d + 3p = 163.5

 

Adding the two equations together, we get...

 

-12p = -54

p = 4.5

 

So, a popcorn costs $4.50. Plug 4.5 in for p in either equation, solve for d, and see how much a drink costs!