During a football game, a concession stand sold a family 2 hamburgers and 2 hotdogs for a total of $13. It sold another family 2 hamburgers and 5 hotdogs for a total of $16. What are the prices of a hamburger and a hotdog?

The price of each hamburger is $3

The price of each hot dogs is $2  .

Step-by-step explanation:

Given as :

The total price of 3 hamburger and 2 hot dogs = $13

The total price of 2 hamburger and 5 hot dogs = $16

Let The price of each hamburger = $x

Let The price of each hot dogs = $y

Now, According to question

3 x + 2 y = 13              A

2 x + 5 y = 16              B

Now, Solving to eq A and B

3 × (2 x + 5 y ) - 2 × (3 x + 2 y ) = 3 × 16 - 2 × 13

Or, (6 x + 15 y) - (6 x + 4 y) = 48 - 26

Or, (6 x - 6 x) + (15 y - 4 y) = 22

Or, 0 + 11 y = 22

∴  y =

i.e y = $2

so, The price of each hot dogs = y = $2

Now, Put the value of y into eq B

i.e 2 x + 5 y = 16

or, 2 x + 5 × 2 = 16

or, 2 x = 16 - 10

or, 2 x = 6

∴  x =

i.e x = $3

So, The price of each hamburger = x = $3

Hence, The price of each hamburger is $3 and  The price of each hot dogs is $2  . Answer