Question

Mohamed and Miguel go to the movie theater and purchase refreshments for their friends. Mohamed spends a total of $18.25 on two bags of popcorn and three

drinks. Miguel spends a total of $27.50 for four bags of popcorn and two drinks.
a) Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.
b) Using your system from part a), determine and state the price of one bag of popcorn and the price of one drink.

Answer 1

If p is the price of a bag of popcorn and d is the price of a drink
2p + 3d = 18.25 Mohamed’s order
4p + 2d = 27.50 Miguel’s order
If we double the first equation
4p + 6d = 36.50
Now subtract the second equation (find the difference between them)
4d = 9.00
d = 2.25
Substitute in the first equation
2p + 3 x 2.25 = 18.25
2p = 18.25 - 6.75 = 11.50
p = 11.50 / 2 = 5.75

Popcorn was $5.75 a bag and drinks were $2.25 each