Question

A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor takes in a total of d dollars, how many cents does a soda cost?

Answer 1

Answer:

$Price\: of \:soda\: is:\:P_s= \frac{100d}{2h+s}$

Step-by-step explanation:

Let

$P_s = cost\: of\: soda$

$P_h=cost \:of\:hotdog$

in dollars.

Then we know that

$P_h=2P_s$

And if the vendor makes total of d dollars:

$hP_h+sP_s=d$

Now substitute the value of $P_h=2P_s$ into this equation and get;

$2hP_s+sP_s=d$

$=P_s(2h+s)=d.$

$\therefore P_s= \frac{d}{2h+s}$

Now this price is in dollars, and to convert it to cents we just multiply it by 100.

$\boxed{\therefore P_s= 100\frac{d}{2h+s} }$

Answer 2

Answer:

The required cost of a soda is $y=100\frac{d}{(2h+s)}$ cents.

Step-by-step explanation:

Given: A vendor sells $h$ hot dogs and $s$ sodas. If a hot dog costs twice as much as a soda.

Let the cost of a hot dog be $x$ dollars and cost of a soda be $y$ dollars.

According to question,

Cost of a hot dog is twice as much as cost of a soda.

$x=2y$                       ...... (1)

Now, total cost of hot dogs and soda given by $x\times h+y\times s=d$ dollars.

$2y\times h+y\times s=d$                    ( From equation 1 )

       $y(2h+s)=d$                

                    $y=\frac{d}{2h+s}$

Therefore, cost of a soda is $y=\frac{d}{(2h+s)}$ dollars.

As we know that,

$1$ dollar $=100$ cents

Hence, Cost of a soda is $y=100\frac{d}{(2h+s)}$ cents.

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