Creating Linear Equations and Inequalities in One Variable

A movie theater is running a promotion: moviegoers can pay an initial fee of $5 and then see as many movies as they want at a rate of $3 per movie. Natasha took advantage of this promotion and paid $23. Which equation could model this scenario?

• 5x + 3 = 23

• 5 + 3x = 23

• 3 + 23x = 5

• 3x + 23 = 5

A movie theater is running a promotion: moviegoers can pay an initial fee of $5 and then see as many movies as they want at a rate of $3 per movie. Natasha took advantage of this promotion and paid $23. How many movies did she see?

• 4

• 6

• 5

• 7

Sam is saving up to buy a new computer. He already has $50 and then starts mowing lawns at $20 per lawn. He wants to earn at least $210. Which equation/inequality would model this situation?

•  $50x+20\le210$ 

•  $50+20x=210$ 

•  $50+20x\le210$ 

•  $50+20x\ge210$ 
  

Sam is saving up to buy a new computer. He already has $50 and then starts mowing lawns at $20 per lawn. He wants to earn at least $210. Which of the following would earn Sam enough money (select all that apply)?

• Mowing 7 lawns

• Mowing 8 lawns

• Mowing 9 lawns

• Mowing 10 lawns

Maria is starting a new job where she earns $10 per hour. Because she wants to save some time for studying and socializing, she tells her boss she can work no more than 20 hours each week. Which inequality would model the number of hours Maria can work?

•  $x\le20$  

•  $10x<20$  

•  $x>20$  

•  $10x\ge20$  

You and your family are attending a sporting event. You park in a parking garage that charges an entrance fee of $4 and then charges $1.50 per hour. Upon leaving you pay $11.50. Which equation would model this scenario?

• 4x + 1.50 = 11.50

• 5.50x = 11.50

• 4 + 1.50x = 11.50

• 4x + 1.50x = 11.50

Nick collects rare coins. He has an initial collection of 20 coins and adds two coins every month. He wants to collect at least 80 coins. Which inequality could model this scenario?

• $20+2x\ge80$

• $20+2x>80$

• $20+2x\le80$

• $20+2x<80$