Determine and state the price of a drink, to the nearest cent.

Question

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

Sophia spends a total of $32.75 on 3 bags of popcorn and 5 drinks.

Paisley spends a total of $51.25 on 6 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.

Answer 1

Hello Captain O. in order to solve this problem, we should first:

let p represent the price of one bag of popcorn

let d represent the price of one drink

We can now set up our equations:

3p + 5d = $32.75

6p + 7d = $51.25

In order to find the price of one drink, we must first find the price of one bag of popcorn in the first equation and plug that value into the second equation and solve for the price of one drink. In order to do so, we must transfer one variable to the right side of the first equation, essentially isolating the variable we desire. Since we have decided to find the price of one bag of popcorn, we must isolate this variable. If we isolate the popcorn variable in the first equation, we will get:

3p + 5d = $32.75

subtract 5d on from both sides of the equation to get:

3p = $32.75 - 5d

The second equation states that there are 6 bags of popcorn, so we must multiply each factor in the first equation by 2. Doing so yields:

2(3p=$32.75 - 5d)

6p= $65.50 - 10 d

We can now find the price of one drink by substituting the algebraic expression we have found for 6p and solving for d.

6p + 7d = $51.25

$65.50 -10d + 7d =$51.25

$65. 50 -3d = $51.25 (we combined like terms here)

Subtracting $65.50 from both sides of the equation to isolate -3d yields:

-3d = -$14.00

we can now divide both sides by -3 to get the final answer.

The final answer is d= $ 4.67

I really hope this helped.