Emily and Lydia go to the movie theater and purchase refreshments for their friends. Emily spends a total of $78.50 on 2 bags of popcorn and 8 drinks. Lydia spends a total of $89.50 on 4 bags of popcorn and 7 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.

The price of one drink is $7.5

The price of one bag of popcorn is $9.25

Step-by-step explanation:

Let us assume,

Emily spends a total of $78.50 on 2 bags of popcorn and 8 drinks.

⇒ 2x + 8y = 78.5  (1)

Lydia spends a total of $89.50 on 4 bags of popcorn and 7 drinks.

⇒ 4x + 7y = 89.5  (2)

To solve for x and y values :

Multiply eq (1) by 2 and subtract eq (2) from eq (1),

  4x + 16y = 157

- (4x + 7y = 89.5)

        9y = 67.5

⇒ y = 67.5/9

⇒ y = 7.5

∴ The price of one drink is $7.5

Substitute y = 7.5 in eq (1),

⇒ 2x + 8(7.5) = 78.5

⇒ 2x + 60 = 78.5

⇒ 2x = 78.5 - 60

⇒ 2x = 18.5

⇒ x = 18.5/2

⇒ x = 9.25

∴ The price of one bag of popcorn is $9.25

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center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.