Question

At a concession stand five hot dogs and four hamburgers cost $12 for hot dogs and five hamburgers cost 1275 the cause of one hot dog in the cost of one hamburger

Answer 1

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 $x.$

And let the cost of one hamburger be $y.$

So, the cost of five hot dogs and four hamburgers:

$5x+4y=12$  

$4y=12-5x$  

Dividing both sides by 4 we get:

$y=3-\frac{5x}{4}$   .......(1)

And, the cost of four hot dogs and five hamburgers:

$4x+5y=12.75$  

Substituting the value of $y$ from equation (1):

$4x+5(3-\frac{5x}{4})=12.75$

$4x+15-\frac{25x}{4}=12.75$

$4x-\frac{25x}{4}+15 =12.75$

$\frac{16x-25x}{4}+15=12.75$

$\frac{-9x}{4} +15=12.75$

Subtracting both sides by 15 we get:

$\frac{-9x}{4}=-2.25$

Multiplying both sides by 4 we get:

$-9x=-9$

Dividing both sides by -9 we get:

$x=1.$

The cost of one hot dog  = $1.

Now, substituting the value of $x$ in equation (1):

$y=3-\frac{5x}{4}$

$y=3-\frac{5\times 1}{4}$

$y=3-\frac{5}{4}$

$y=3-1.25$

$y=1.75.$

The cost of one hamburger = $1.75.

Therefore, the cost of one hot dog $1 and the cost of one hamburger is $1.75.