At a concession stand, five hot dogs and four hamburgers cost $14; four hot dogs and five hamburgers cost $15.25. find the cost of one hot dog and one hamburger

Answer 1

These really confused me at first, too!

5d + 4h = 14

4d + 5h = 15.25

We need the coefficients of d or h to be opposites so that they add up to zero. What if we make the d coefficients 20 and -20?

4(5d + 4h) = 4(14)

-5(4d + 5h) = -5(15.25)

20d + 16h = 56

-20d - 25h = -76.25

Now, if we add the two equations together...

-9h = -20.25

-9h/-9 = 60.25/9

h = $2.25

5d + 4(2.25) = 14

4d + 9 = 14

4d = 5

d = $1.25

Answer 2

5D + 4H = 14

4D + 5H = 15.25

20D + 25H = 76.25

20D + 16H = 56

9H= 20.25

H= $2.25 = cost of one Hamburger

5D =14 -4(2.25) = 14-9 = $5

D = $1.00 = cost of one hotDog

cost of 1 of each = $3.25