#11 step by step please

Question

Games at the carnival cost $3.50 each. The prizes awarded to winners cost the owner $135. How many games must be played for the owner of the game to make at least $45?

Answer 1

let x = number of games played

 

you are trying to find value of x so that owner makes AT LEAST $45. So $45 is the goal so that is on one side of the equation

 

45< 

 

then you need to find how many games will be played at 3.50 a piece, so the profit to the owner would be 3.50*x 

 

so 45 < 3.50x 

 

however the owner has a cost of -135 so that needs to come out of the profits

 

so 45 < 3.50x - 135

 

now you just need to solve for the x in the equation

 

45       < 3.50x - 135

+135               +135

 

180 < 3.50x 

 

divide each side by 3.50 

 

x < 51.5 (approximately) 

 

so number of games to make money is 52 games since you can't sell half a game