Question

at a basketball game, a vender sold a combined total of 166 sodas and hot dogs. The number of hot dogs sold was 54 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold. ​

Answer 1

The best way to solve these sorts of problems that involve two factors of unknown quantities but with certain properties is to use equations:

Let's set some variables

• h: # of hot dogs sold
• s: # of sodas sold

Now based on the information given by the question, let's set up some equations:

• vender sold a combined total of 166 sodas and hot dog

⇒
`s + h = 166`

• number of hot dogs sold was 54 less than the number of sodas sold

⇒ h = s - 54

Now lets put the equation together

s + h = 166 -- equation 1

h = s - 54 -- equation 2

Solve:

Plug the value of h from equation 2 into equation 1

s + (s - 54) = 166

2s - 54 = 166

2s = 220

s = 110 -- equation 3

Plug the value of s from equation 3 into equation 2

h = 110 - 54 = 56

h = 56

Therefore:

• number of sodas sold: 110
• number of hot dogs sold: 56

Hope that helps!