At school athletic events you can buy 3 drinks and 2 hot dogs for $4.80 or you can buy 1 drink and 1 hot dog for $2.00. how much does 1 hot dog cost?

Let the cost of each drink is $x and the cost of each hot dog is $y.
According to the given data, 3 drinks and 2 hot dogs cost $4.80. In equation form, we can write it as:



1 drink and 1 hot dog costs $2.00. In equation form, we can write it as:




Using this value of x in first equation, we get:



Thus the cost of one hot dog is $1.20

This is a question in which simultaneous equations are used to find out the answer.
There are 2 unknown values which we name as x and y
x - price of a drink
y - price of a hotdog

although we don't know the values of the above 2 terms x and y, we know the relationships of these 2 terms as the the sums of these 2 have been given 
therefore we can build 2 equations using the information we have been given 

3 drinks = 3*x and 2 hotdogs = 2*y 
we build the first equation using this information 

1 - 3x + 2y = $ 4.80 
 
1 drink and 1 hotdog costs $2.00
we can build the second equation using this information

2 - x + y = $ 2.00

first we have to find out the value of one unknown term, for this we need to eliminate the second unknown so that we are left with one unknown term in the equation
if we want to eliminate y, 2nd equation should be multiplied by 2
2. 2(x + y = 2)
    the answer after multiplying all the terms by 2, lets call that the 3rd equation   
 
3.    2x + 2y = 4
when we subtract 1st from the 2nd equation,
3x + 2y = 4.8 ( - ) 2x + 2y = 4
lets subtract like terms from like terms
3x - 2x = x
2y - 2y = 0
4.8 - 4 = 0.8
after subtracting the final equation looks like this;
x = 0.8
since we know x now, substitute x in the equation 2
x + y = 2
0.8 + y = 2
to find out y 
y = 2 - 0.8
y = 1.2
Therefore price of a drink is $0.80
and price of hotdog is $1.20