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Video: Writing and Solving Linear Inequalities in a Real-World Context

Kathryn Kingham

Anthony earns $6.75 an hour waiting on tables. He is saving money to buy a new video game which costs $27. Write an inequality to find how many hours Anthony must work to buy the game, and then solve it.

02:08

Video Transcript

Anthony earns six dollars and 75 cents per hour waiting on tables. He is saving money to buy a new video game, which costs 27 dollars. Write an inequality to find how many hours Anthony must work to buy the game, and then solve it.

Our question is asking us to do two things: the first thing write an inequality and the second thing solve that inequality. Our inequality is to figure out how many hours Anthony must work to buy the game.

The money Anthony gets from working must be greater than or equal to the cost of the video game, and Anthony makes six dollars and 75 cents per hour. That amount must be greater than or equal to 27 dollars, which is the cost of the video game.

Letโ€™s say that ๐‘ฅ is a number of hours Anthony works. Then we would say six dollars and 75 cents times ๐‘ฅ must be greater than or equal to 27 dollars. What we have now is an inequality. So weโ€™ve finished the first step of this problem.

Our second step asks us to solve this inequality to figure out how many hours Anthony must work. We need to isolate our ๐‘ฅ by dividing both sides of the equation by six dollars and 75 cents. The left side of the equation is left with ๐‘ฅ. 27 divided by 6.75 equals four.

Anthony must work four or more hours to save enough money to buy his video game. And this is the inequality we used to figure that out. 6.75 multiplied by ๐‘ฅ must be greater than or equal to 27.