The Jacobsen family bought concessions at the state fair. • Each hot dog costs $1.25. • Each hamburger costs $2.50. • The family bought a total of 13 hot dogs and hamburgers. • The family spent $22.50 on the hot dogs and hamburgers. Enter the number of hot dogs and hamburgers the Jacobsen family bought. Hot dogs hamburgers

The family bought 8 hot dogs and 5 hamburguers.

Step-by-step explanation:

We'll call the amount of hamburguers as 'x' and the amount of hot dogs as 'y'. Since the family bought 13 hot dogs and hamburguers we have:

x + y = 13

The family spent a total of 22.5, if each hot dog costs 1.25 and each hamburguer costs 2.5, we have:

2.5*x + 1.25*y = 22.5

We now have two equations and two variables so we can build a system as state bellow:

x + y = 13

2.5*x + 1.25*y = 22.5

From the first equation we have x = 13 - y. We can use this value on the second equation to solve for y:

2.5*(13 - y) + 1.25*y = 22.5

32.5 - 2.5*y + 1.25*y = 22.5

-2.5*y + 1.25*y = 22.5 - 32.5

-1.25*y = -10

y = 10/1.25 = 8

So x = 13 - y = 13 - 8 = 5.

The family bought 8 hot dogs and 5 hamburguers.