Kevin and Levi go to the movie theater and purchase refreshments for their friends. Kevin spends a total of $44.50 on 3 bags of
popcorn and 4 drinks. Levi spends a total of $84.00 on 4 bags of popcorn and 8 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.
Hi, to answer this question we have to write a system of equations:
The total cost for Kevin (44.50) is equal to the product of the number of popcorn bags bought (x ) and the price of each bag, plus the product of the number of drinks purchased (y) and the price of each drink (y).
Mathematically speaking
Kevin : 44.50 = 3 x + 4 y
Using the same process for Levi:
Levi : 84= 4x +8 y
The system is
44.50 = 3 x + 4 y (k)
84= 4x +8 y (L)
If we multiply Kevin's equation by 2 and subtract it to Levi's equation:
