Sophia and skylar go to the movie theater and purchase refreshments for their friends.

sophia spends a total of $98.75 on 3 bags of popcorn and 7 drinks.

skylar spends a total of $218.25 on 15 bags of popcorn and 6 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.

3p + 7d = 98.75 and 15p + 6d = 218.25 are the system of equations that can be used to find the price of one bag of popcorn and the price of one drink

The price of 1 drink is $ 9.5

Solution:

Let "p" be the price of 1 bag of popcorn

Let "d" be the price of 1 drink

Given that,

Sophia spends a total of $98.75 on 3 bags of popcorn and 7 drinks

Therefore, we can frame a equation as,

3 x price of 1 bag of popcorn + 7 x price of 1 drink = 98.75

3p + 7d = 98.75 -------- eqn 1

Skylar spends a total of $218.25 on 15 bags of popcorn and 6 drinks

15 x price of 1 bag of popcorn + 6 x price of 1 drink = 218.25

15p + 6d = 218.25 -------- eqn 2

Thus eqn 1 and eqn 2 are the system of equations that can be used to find the price of one bag of popcorn and the price of one drink

Determine and state the price of a drink:

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 5

15p + 35d = 493.75 ------ eqn 3

Subtract eqn 2 from eqn 3

15p + 35d = 493.75

15p + 6d = 218.25

( - ) -------------------------------

29d = 275.5

d = 9.5

Substitute d = 9.5 in eqn 1

3p + 7(9.5) = 98.75

3p + 66.5 = 98.75

3p = 32.25

p = 10.75

Thus the price of 1 drink is $ 9.5

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

step-by-step explanation: