linear system

Question

Angel and Alexander go to the movie theater and purchase refreshments for their friends. Angel spends a total of $32.50 on 3 drinks and 2 bags of popcorn. Alexander spends a total of $72.50 on 6 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

Let x = the cost of one drink

Let y = the cost of one bag of popcorn

3x + 2y = 32.50         Multiply this equation by -2 and add it to the next equation.

6x + 10y = 72.50

-6x - 4y = -65.00

        6y = 7.50

          y = $1.25

3x + 2(1.25) = 32.50

3x + 2.50 = 32.50

3x = 30

x = $10