Khloe and Lily go to the movie theater and purchase refreshments for their friends. Khloe spends a total of $79.50 on 8 drinks and 2 bags of popcorn. Lily spends a total of $82.50 on 5 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 bag of popcorn, to the nearest cent.

3.75 dollars

step 1 ; set up the system of equations

8d + 2p=79.50

5d + 10p=82.50

step 2:Multiply the first equation in order to create cancellation

-5(8d+2p=79.50)

5d+10p=82.50

step 3:add to eliminate a variable .

-40d-10p=-397.50

+(5d+10p=82.50)

-35d        =-315.00

step 4;Solve for the remaining variable.

(y/x means fraction)        -35d/-35 = -315/-35

                            d=9.00

Step 5: substitute the known value into the original equation to solve for the second variable.

8(9)+2p=79.50

72+2y=79.50

-72        -72

        2p/2 = 7.50/2

          p=3.75

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

step-by-step explanation: