I need help with a word problem

Question

At a concession stand, five hot dogs and four hamburgers cost $17.75; four hot dogs and five hamburgers cost $18.25. Find the cost of one hot dog and the cost of one hamburger.

 

Answer 1

let x be cost of a hotdog

let y be cost of hamburger

 

so,

 

5x + 4y = 17.75                    eq. 1

4x + 5y = 18.25                    eq. 2

 

manipulate eq. 1 so solve for x:

 

5x = 17.75 - 4y

 

x = 17.75/5 - (4/5)y

 

x = 3.55 - (4/5)y                  eq. 3

 

substitute eq. 3 to eq. 2:

 

4(3.55 - (4/5)y) + 5y = 18.25

 

14.2 - (16/5)y + 5y = 18.25

 

14.2 + (9/5)y = 18.25

 

(9/5)y = 18.25 - 14.2

 

4.05= (9/5)y

 

y = 2.25

 

x = 3.55 - (4/5)(2.25)

 

x = 1.75

 

hotdog costs $1.75

hamburger costs $2.25

 

 

 

 

 

 

 

 

 

 

 

Answer 2

Cost of one hot dog = $1.75

Cost of one hamburger = $2.25