Question

Makayla and Caroline go to the movie theater and purchase refreshments for their friends. Makayla spends a total of $49.00 on 9 bags of popcorn and 8 drinks. Caroline spends a total of $17.25 on 3 bags of popcorn and 3 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 drink, to the nearest cent.

Answer 1

Answer:

Let the cost of each popcorn bag be x and cost of each  drink be y

Cost of 9 bags of Popcorn= 9 x

Cost of 8 drinks be = 8 y

Total money spent by Makayla = $ 49

According to Question

9 x + 8 y= 49..................... equation (1)

Similarly , cost of 3 popcorn = 3 x

Cost of 3 drinks= 3 y

Total money spent by Caroline= $ 17.25

According to Question

3 x+ 3 y= $ 17.25...................equation(2)

We can solve above equation by using elimination method

Multiply equation (2) by 3

9 x + 9 y =  51.75..................equation(3)

9 x + 8 y= 49..................... equation (1)

Subtraction equation (1 ) from equation(3)

y = 2.75

put value of y  in any equation (2)

we get

3 x + 3 × 2.75 = 17.25

3 x +   8.25 = 17.25

3 x = 17.25 - 8.25

3 x = 9

x = 3

Hence, cost of each popcorn bag $ 3 cost of each popcorn bag is also $ 3 (approx)