At a concession stand, five hot dogs and two hamburgers cost $9.25 ; two hot dogs and five hamburgers cost $10.00. Find the cost of one hot dog and the cost of one hamburger.

hot dogs - $1.25

hamburgers - $1.50

Step-by-step explanation:

let hot dogs be x and hamburgers be y∀

five hot dogs and two hamburgers cost $9.25

5x + 2y = $9.25 (eq. 1)

5x=9.25-2y

divide both sides by 5x

x = 1.85-0.4 (insert this in eq. 2)

two hotdogs and five hamburgers cost $10.00

2x + 5y = $10.00 (eq. 2)

2 * (1.85-0.4) + 5y=10.00

3.7 - 0.8 + 5y = 10.00

-0.8+5y=10.00-3.7

4.2y=6.3

divide both sides by 4.2 to evaluate the variable

6.3 divided by 4.2

y=1.50

now find x

x=1.85-0.4*1.5

x=1.85-0.6

x = 1.25