Respuesta :
Answer : The cost of one hot hot dog and the cost of one hamburger is, $3.75
Step-by-step explanation :
Let the cost of hot dog be, 'x' and hamburger be, 'y'.
Given:
5 hot dogs and 2 hamburgers cost is, $12.00. The equation will be :
[tex]5x+2y=12[/tex] ..............(1)
2 hot dogs and 5 hamburgers cost is, $14.25. The equation will be :
[tex]2x+5y=14.25[/tex] ..............(2)
Now we have to determine the value of 'x' and 'y' by using substitution method.
[tex]5x+2y=12[/tex]
[tex]x=\frac{12-2y}{5}[/tex] ............(3)
Now put equation 3 in 2, we get:
[tex]2x+5y=14.25[/tex]
[tex]2(\frac{12-2y}{5})+5y=14.25[/tex]
[tex]\frac{24-4y}{5}+5y=14.25[/tex]
[tex]24-4y+25y=71.25[/tex]
[tex]21y=47.25[/tex]
y = 2.25
Now put the value of 'y' in 3, we get:
[tex]x=\frac{12-2y}{5}[/tex]
[tex]x=\frac{12-2(2.25)}{5}[/tex]
[tex]x=\frac{12-4.5}{5}[/tex]
[tex]x=\frac{7.5}{5}[/tex]
x = 1.5
Cost of hot dog = x = $1.5
Cost of hamburger = y = $2.25
Now we have to calculate the cost of one hot hot dog and the cost of one hamburger.
Cost of 1 hot hot dog and 1 hamburger = x + y
Cost of 1 hot hot dog and 1 hamburger = $1.5 + $2.25
Cost of 1 hot hot dog and 1 hamburger = $3.75
Therefore, the cost of one hot hot dog and the cost of one hamburger is, $3.75
