seven hot dog and two hamburgers cost ​$11.75 and two hot dogs and seven hamburgers cost ​$13.00. whats the of one hot dog and the cost of one hamburger

Question

At a concession stand, seven hot dog and two hamburgers cost $11.75 and two hot dogs and seven hamburgers cost $13.00. Find the cost of one hot dog and the cost of one hamburger

Answer 1

cost of 1 hot dog = x

 

cost of 1 hamburger = y

 

seven hot dog and two hamburgers cost $11.75

7x+ 2y=11.75

 

two hot dogs and seven hamburgers cost $13.00.

2x+7y = 13

 

7x+2y=11.75   _______eq 1

2x+7y=13       _______eq 2

 

solve these 2 equation simulteniously

multiply equation 1 with 2 and equation 2 with 7 and subtract eq 2 from eq 1

 

 

14x+4y=23.5

14x +49y = 91

____________

       -45y = 67.5

          y= 1.5

subsitute value of y in eq 1

 

7x+2y=11.75

7x+2(1.5) =11.75

7x+3 =11.75

7x = 8.75

x=1.25

 

cost of 1 hot dog = x =$1.25

cost of 1 hamburger = y=$1.5