Question

At a concession​ stand,three hot dog(s) and two hamburger(s) cost ​$8.25​;two hot dog(s) and three hamburger(s) cost ​$8.00. Find the cost of one hot dog and the cost of one hamburger. What is the cost of one hot dog​? $_____

Answer 1

The cost of one hot dog and the cost of one hamburger is $3.25

The cost of one hot dog is $1.75

Explanation:

Let the number of hot dogs be represented by d and hamburgers be h

3d + 2h = 8.25 ----- eqn(I)

2d + 3h = 8.00 ----- eqn(II)

From eqn(I): d = (8.25 - 2h)/3

substitute the expression for d into eqn(II)

2d + 3h = 8

2(8.25 - 2h)/3 + 3h = 8

(16.50 - 4h) + 3h(3) = 8(3)

16.50 - 4h + 9h = 24

5h = 24 - 16.50

5h = 7.50

h = 7.50/5 = 1.50

One hamburger costs $1.50

d = (8.25 - 2h)/3 = (8.25 - 2×1.50)/3 = (8.25 - 3.00)/3 = 5.25/3 = 1.75

One hot dog costs $1.75

Cost of one hot dog and cost of one hamburger = $1.75 + $1.50 = $3.25