algebra word problems

Question

a clown is preparing for a party by inflating one balloon for every invited guest. Just when she has half of the necessary balloons inflated, 3 of them pop.  She inflates 5 more balloons, and 2 pop. Then 6 balloons are carried away by the wind. She finishes by inflating 16 more balloons, then learns that only 12 guests will attend the party.  How many extra balloons did the clown inflate?

Answer 1

step 1: figure out how many balloons were inflated total

x represents the total balloons inflated

 

 x/2 - 3 + 5 - 2 - 6 + 16 = x    simplify left hand side

 

 x/2 + 10 = x                         solve for x

-x/2          -x/2

 

10 = x/2

*2    *2

 

x = try and work through the above math to get this yourself

 

step 2: subtract to figure out how many were extra

(x balloons inflated) - (12 needed) = answer