How many hotdogs and how many cans of soda were sold? Mitchell works at a concession stand selling hotdogs and cans of soda. A hotdog costs $3.00 and a can of soda costs $1.00. One night, he notices that he sold a total of 350 items and collected a total of $624.

Question

imstuck · Answer

First you have to relate the number of hot dogs and cans of soda to the total number of items sold.  This will be equation 1.  Then you relate the money part of it...how much each hot dog sells for, how much each can of soda sells for, then have those relate to the total amount of money made.  This is the second equation.  You will have a system of equations for which you will solve for the variables to get your answer.  First one relating the number of each sold looks like this:

imstuck · Answer

|dw:1411953868957:dw|

imstuck · Answer

Then we relate the money that each costs to how much was actually made, which is $624.  The number of hot dogs, which we don't know, at $3 apiece, is represented by 3h, which means that each hot dog costs $3.  The cans of soda sell for $1 apiece, so that can be represented by 1s (or just s).  Adding what they cost together is equal to 624.  That second equation looks like this:

imstuck · Answer

|dw:1411954038430:dw|

imstuck · Answer

Now you have a system of equations that needs to be solved for both h and s.  Do this one variable at a time.  I recommend doing it using the substitution method. Are you familiar with it?  I'm sure you are if you are doing these in class.

anonymous · Answer

Yes, I am. So far I've gotten to... 
hotdogs=h
cans of soda=s

s + h = 350
3h + 1s = 624

s = 350 - h
3h + 1(350 - h) = 624
3h + 350 - h = 624

2h = 974
h = 487

anonymous · Answer

But i just wasn't able to find a number for s because i kept getting a negative result

anonymous · Answer

@IMStuck

texaschic101 · Answer

s + h = 350 --> s = 350 - h
3h + s = 624

3h + 350 - h = 624 -- subtract 350 from both sides
3h - h = 624 - 350 -- combine like terms
2h = 274
h = 274/2
h = 137

s + h = 350
s + 137 = 350
s = 350 - 137
s = 213

check..
3h + s = 624
3(137) + 213 = 624
411 + 213 = 624
624 = 624 (correct)

137 hotdogs (h) and 213 sodas (s) were sold

texaschic101 · Answer

what you did was added the 350 instead of subtracting it