Question

Julia went to the movies and bought one jumbo popcorn and two chocolate chip cookies for $5:00. Marvin went to the same movie and bought one jumbo popcorn and four chocolate chip cookies for $6.00. How much does each item cost.

Answer 1

The jumbo popcorn costs $4.00 and each chocolate chip cookie costs $0.50.

Step-by-step explanation:

To find the cost of each item, let's assign variables to the prices. Let x represent the cost of the jumbo popcorn and y represent the cost of each chocolate chip cookie.

From the given information, we know that Julia bought 1 jumbo popcorn and 2 chocolate chip cookies for $5.00, and Marvin bought 1 jumbo popcorn and 4 chocolate chip cookies for $6.00.

Using our variables, we can create two equations to represent these situations:

1. x + 2y = 5
2. x + 4y = 6

By solving these equations simultaneously, we can find the values of x and y, which represent the cost of each item.

Step 1: Solve equation (1) for x: x = 5 - 2y

Step 2: Substitute the value of x in equation (2): 5 - 2y + 4y = 6

Step 3: Simplify and solve for y: 5 + 2y = 6

Step 4: Subtract 5 from both sides: 2y = 1

Step 5: Divide both sides by 2: y = 0.50

Now that we have the value of y, we can substitute it back into equation (1) to find the value of x:

x + 2(0.50) = 5

x + 1 = 5

x = 4

Therefore, the jumbo popcorn costs $4.00 and each chocolate chip cookie costs $0.50.

Answer 2

In order to solve for this, let's start by assigning two variables.

'p' will represent the price of popcorn? and 'c' will represent the price of a cookie.

Now that we have these two variables, we can use the given statements to make two equations:

p + 2c = 500 ("Julia...bought one jumbo popcorn and two chocolate chip cookies for $5.00")
p + 4c = 600 ("Marvin went to the same movie and bought one jumbo popcorn and four chocolate chip cookies for $6.00")

In order to solve for the variables, we can use the subtraction method.

p + 2c = 500
-p - 4c = -600
___________
-2c = -100

Divide both sides by -2:
c = 50

Now that we know that a cookie costs 50 cents, we can input it into one of our equations to solve for the price of popcorn:

p + 2(50) = 500
p + 100 = 500
p = 400

Jumbo popcorn costs $4.00, and cookies cost $0.50.

Good luck! If you need me to explain anything in more detail, just ask :))
-T.B.