Each game at a carnival costs $0.50, or you can pay $15 and play unlimited amount of games. write and solve an inequality to find how many times you should play at a game so that the unlimited game play is less than paying each time. interpret the solution. plz thx

  If we play games more than 30 games, amount paid for unlimited games will be less than paying each time.

   Let the number of games played at the rate of $0.50 per game = x

"If the cost of playing unlimited games is less than the paying each time",

Inequality for this situation will be,

15 < 0.50x

30 < x

This interprets that "if we play games more than 30 games, amount paid for unlimited games will be less than paying each time".

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Play at least 30 times

Step-by-step explanation:

The answer to this question is found by equating the "flat rate" $15 to the direct proportion function g(x) = ($0.50/game)x.  Here x represents the number of games played.

So, we solve the equation

$15 = ($0.50/game)x for x.  Dividing both sides by $0.50/game, we get:

  $15

= 30 games

($0.50/game)

After 30 games have been played, the unlimited game plan is cheaper than paying for each game one at a time.