Question

Roger and Junior went to 2 baseball games this past weekend. At the first game, they bought 5 hot dogs and 2 orders of nachos and spent $13.75. At the second game, they bought 4 hot dogs and 3 orders of nachos and spent $14.50. What was the price of each food item?

a) Hot dogs: $2.25, Nachos: $3.25
b) Hot dogs: $2.50, Nachos: $3.00
c) Hot dogs: $3.00, Nachos: $2.25
d) Hot dogs: $3.25, Nachos: $2.50

Answer 1

To find the price of each food item, set up a system of equations and solve using elimination. The price of a hot dog is $1.75 and the price of an order of nachos is $2.50.

Step-by-step explanation:

To find the price of each food item, we can set up a system of equations based on the information given. Let's assign variables to represent the price of hot dogs and nachos:

Let x be the price of a hot dog.

Let y be the price of an order of nachos.

Using the information from the first game, we can write the equation:

5x + 2y = 13.75

Using the information from the second game, we can write the equation:

4x + 3y = 14.50

Now, we can solve this system of equations using any method, such as substitution or elimination. Let's use elimination:

Multiply the first equation by 3 and the second equation by 2 to make the coefficients of y the same:

15x + 6y = 41.25

8x + 6y = 29

Subtract the second equation from the first equation:

7x = 12.25

Divide both sides of the equation by 7 to solve for x:

x = 1.75

Substitute this value of x into one of the original equations to solve for y:

5(1.75) + 2y = 13.75

8.75 + 2y = 13.75

Subtract 8.75 from both sides of the equation:

2y = 5

Divide both sides of the equation by 2 to solve for y:

y = 2.50

Therefore, the price of a hot dog is $1.75 and the price of an order of nachos is $2.50.