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.

44.50 = 3 x + 4 y

84= 4x +8 y

each popcorn bag costs $2.5

Step-by-step explanation:

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:

89 = 6x +8y

          -

( 84= 4x +8 y)

5 = 2x

solving for x

5/2= x

2.5 =x

each popcorn  costs $2.5

42.4

step-by-step explanation:

convert to decimal

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15