Respuesta :
Answer:
The cost of one hot dog $1 and the cost of one hamburger is $1.75.
Step-by-step explanation:
Given:
At a concession stand five hot dogs and four hamburgers cost $12.
Four hot dogs and five hamburgers cost $12.75.
Now, to find the cost of one hot dog and the cost of one hamburger.
Let the cost of one hot dog be [tex]x.[/tex]
And let the cost of one hamburger be [tex]y.[/tex]
So, the cost of five hot dogs and four hamburgers:
[tex]5x+4y=12\\\\[/tex]
[tex]4y=12-5x[/tex]
Dividing both sides by 4 we get:
[tex]y=3-\frac{5x}{4}[/tex] .......(1)
And, the cost of four hot dogs and five hamburgers:
[tex]4x+5y=12.75[/tex]
Substituting the value of [tex]y[/tex] from equation (1):
[tex]4x+5(3-\frac{5x}{4})=12.75[/tex]
[tex]4x+15-\frac{25x}{4}=12.75[/tex]
[tex]4x-\frac{25x}{4}+15 =12.75[/tex]
[tex]\frac{16x-25x}{4}+15=12.75[/tex]
[tex]\frac{-9x}{4} +15=12.75[/tex]
Subtracting both sides by 15 we get:
[tex]\frac{-9x}{4}=-2.25[/tex]
Multiplying both sides by 4 we get:
[tex]-9x=-9[/tex]
Dividing both sides by -9 we get:
[tex]x=1.[/tex]
The cost of one hot dog = $1.
Now, substituting the value of [tex]x[/tex] in equation (1):
[tex]y=3-\frac{5x}{4}[/tex]
[tex]y=3-\frac{5\times 1}{4}[/tex]
[tex]y=3-\frac{5}{4}[/tex]
[tex]y=3-1.25[/tex]
[tex]y=1.75.[/tex]
The cost of one hamburger = $1.75.
Therefore, the cost of one hot dog $1 and the cost of one hamburger is $1.75.
