Question

The concession stand at a school basketball tournament sells hot dogs, hamburgers and chicken sandwiches. During one game, the stand sold 16 hot dogs, 14 hamburgers, and 8 chicken sandwiches for a total of $99.50. During a second game, the stands sold 10 hotdogs, 13 hamburgers and 5 chicken sandwiches for a total of $76.00. During a third game, the stand sold 4 hot dogs, 7 hamburgers and 7 chicken sandwiches for a total of $57.50.

Answer 1

The prices per item at the concession stand during each game are as follows:

First game:

• Hot dog: $6.17
• Hamburger: $7.03
• Chicken sandwich: $12.44

Second game:

• Hot dog: $7.60
• Hamburger: $5.85
• Chicken sandwich: $15.20

Third game:

• Hot dog: $14.38
• Hamburger: $8.21
• Chicken sandwich: $8.21

Step-by-step explanation:

To determine the prices of each item sold at the concession stand, we need to find the total revenue from each game and then divide that by the number of items sold for each item type.

During the first game:

Total revenue = $99.50

of hot dogs = 16

Number of hamburgers = 14

Number of chicken sandwiches = 8

During the second game:

Total revenue = $76.00

Number of hot dogs = 10

Number of hamburgers = 13

Number of chicken sandwiches = 5

During the third game:

Total revenue = $57.50

Number of hot dogs = 4

Number of hamburgers = 7

Number of chicken sandwiches = 7

Now, we will calculate the prices per item for each game.

First Game:

• Hot dog price = $99.50 / 16 = $6.17
• Hamburger price = $99.50 / 14 = $7.03
• Chicken sandwich price = $99.50 / 8 = $12.44

Second Game:

• Hot dog price = $76.00 / 10 = $7.60
• Hamburger price = $76.00 / 13 = $5.85
• Chicken sandwich price = $76.00 / 5 = $15.20

Third Game:

• Hot dog price = $57.50 / 4 = $14.38
• Hamburger price = $57.50 / 7 = $8.21
• Chicken sandwich price = $57.50 / 7 = $8.21

Answer 2

The price of hot dogs is $1.03, price of hamburgers is $3.66 and price of chicken sandwiches is $3.96.

How the prices of the items were calculated.

Let's denote the price of hot dogs to be k, price of hamburgers to be w and price of chicken sandwiches to be t.

During one game:

Price of hot dogs= 16

Price of hamburgers = 14

Price of chicken = 8

Total revenue = $99.50

16k +14w +8t = $99.50.............................1

During second game:

Price of hot dogs = 10

Price of hamburgers = 13

Price of chicken = 5

Total revenue = $76.00

10k +13w +5t = $76.00...............................2

During third game:

Price of hotdogs = 4

Price of hamburgers = 7

Price of chicken = 7

Total revenue = $57.50

4k +7w +7t = $57.50..................................3

Let's solve the equations simultaneously

16k +14w +8t=99.50.

10k +13w +5t =76.00

4k +7w +7t =57.50

Multiply equation 3 by 2 subtract equation 1 from the result to eliminate w.

8k +14w +14t =115

Subtract equation 1 from the result

-8k +6t =15.5

multiplying equation 2 by 7 and 3 by 13

70k +91w +35t =532

52k +91w +91t =747.5

Subtracting the equation 52k +91w +91t =747.5 from 70k +91w +35t =532.

18k +56t =215.5

-8k +6t =15.5-------------------------4

18k +56t =215.5---------------------5

18(6t-15.5)/8 +56t=215.5

54t-139.5+224t=215.4*4

278t=862+139.5

t=3.96

Substitute t = 3.96 into -8k +6t =15.5

k =(6t -15.5)/8

k =(6*3.96-15.5)/8

k =8.26/8

k =1.03

Substitute these values of k and t in any of the above equation.

4(1.03) +7w +7(3.96) =57.50

4.12 + 7w + 27.72 = 57.50

7w = 25.66

w = 25.66/7

= 3.67

Therefore, the price of hot dogs is $1.03, price of hamburgers is $3.66 and price of chicken sandwiches is $3.96