# What does a soda cost?

1. Jul 9, 2004

### Monique

Staff Emeritus
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?

Good luck keep in mind, this is a question taken from an actual test that should be solved in 60-90 seconds..

2. Jul 9, 2004

### Gokul43201

Staff Emeritus
100d = h(2x) + s(x) = x(2h + s)
So, x = 100d/(2h+s).

Surely, there's a catch somewhere, that I'm missing !

3. Jul 9, 2004

### Brennen

Monique, its me from the IQ post. hell, i figured that out, i thought there would have had to have been a catch to it more complex than that. if thats all you were looking for then i got that. sorry.

4. Jul 10, 2004

### vikasj007

hey monique
although i am trying to figure it out, i would like to know if you are an indian, or do you have an indian connection, coz, that signature line is in hindi. which is not very common.

5. Jul 10, 2004

### Monique

Staff Emeritus
Hey vikasj007, aap kaise hai? I'm not really indian.

Goluk has the right solution!

6. Jul 10, 2004

### vikasj007

if this is the right solution, then i don't get it that how is it a brain teaser. all he did was to form an equation,. and took all but one variable on one side. i thought there was something more to it than that.
even gokul feels that there is a catch. :rofl:

7. Jul 10, 2004

### rayjohn01

soda cost

Whatever your prepared to pay for it ---- when your thirsty. Ray

8. Jul 11, 2004

### The Bob

s = 2h
Σs + Σh = d
1/3d ≈ s (not likely)
2/3d ≈ h (not likely)

What more can be got from the question? There is no price or capacity of the vendor and no number of people that used it. Gokul used 100d as an approx but it is right. How?

9. Jul 12, 2004

### Gokul43201

Staff Emeritus
Not sure what you mean by this, but ...

It does not say anuwhere, that s= 2h. How did you arrive at this ?
100d is not an approximation. It is exactly the amount taken in (measured in cents).
Let x be the cost of the soda. Then the cost of a hot dog is 2x (in cents).

10. Jul 12, 2004

### The Bob

Sorry it is h = 2s as a hot dog is twice as much as a soda. I still don't get it though. Sorry.

11. Jul 12, 2004

### EFischer

The Bob, s and h are the number of sodas and hot dogs, not the price.

12. Jul 13, 2004

### The Bob

Yes I know. Ok my bad. But I still don't get it.

13. Jul 13, 2004

### Gokul43201

Staff Emeritus
Let x (cents) be the cost of one soda. Then, if s number of sodas are sold, the amount made is xs (in cents).

Now, the cost of one hotdog will be 2x, since it is twice as expensive as a soda. The number of hotdogs sold is h. So, the earnings from hotdogs is 2xh.

Total earnings = xs + 2xh = x(s+2h).

But we are told that the total earnings is d dollars, which is the same as 100d cents.

Thus, 100d = x(s+2h). Rearranging, we get : x = 100d/(s+2h), which is what we want to find out.

14. Jul 13, 2004

### The Bob

Oh I get it. Sorry Gokul. I am as thick as a two by four.