Writing Equations and Inequalities

A pilot takes a taxi from the airport to a hotel. The taxi driver charges a $2.50 initial charge plus $2.65 per mile. Which equation can be used to find y, the total cost of the trip, if x represents the number of miles of the trip?

• y = 2.50x + 2.65

• y = 2.65(x + 2.50)

• y = 2.65x - 2.50

• y = 2.65x + 2.50

Chad wrote this equation which can be used to correctly solve one of the word problems below. t = 2y + 2.57 Which of the word problems can best be solved by Chad’s equation?

• Today’s price of a barrel of oil, t, is $2.57 more than twice y, the price of a barrel of oil one year ago. Oil was $33.46 per barrel one year ago. What is the price, t, of a barrel of oil today?

• The price of a gallon of gasoline one year ago, y, is $2.57 less than twice t, the price of a gallon of gasoline today. Gasoline is $3.46 per gallon today. What was the price, t, of a gallon of gasoline one year ago?

• Today’s price of a barrel of oil, t, is $2.57 more than y, the price of a barrel of oil 2 years ago. Oil was $33.46 per barrel 2 years ago. What is the price, t, of a barrel of oil today?

• The price of a gallon of gasoline one year ago, y, is $2.57 more than twice t, the price of a gallon of gasoline today. Gasoline is $3.46 per gallon today. What is the price, t, of a gallon of gasoline today?

The model represents an Inequality.

• A) Adam earns $60 per day plus $3 for every item he sells in a store. How many items he needs to sell in a day to earn at least $75?

• B) Adam earns $3 per day plus $60 for every item he sells in a store. How many items he needs to sell in a day to earn at least $75?

• C) Adam earns $60 per day plus $3 for every item he sells in a store. How many items he needs to sell in a day to earn at most $75?

• D) Adam earns $3 per day plus $60 for every item he sells in a store. How many items he needs to sell in a day to earn at most $75?

• F

• G

• H

• J

• A) Felicia has 12 buttons in her collection. She will collect 29 new buttons every year. Felicia collects buttons for k years. For what values of k will Felicia have at least 120 buttons?

• B) Felicia has 29 buttons in her collection. She will collect 12 new buttons every year. Felicia collects buttons for k years. For what values of k will Felicia have at least 120 buttons?

• C) Felicia has 29 buttons in her collection. She will collect 12 new buttons every year. Felicia collects buttons for k years. For what values of k will Felicia have at most 120 buttons?

• D) Felicia has 12 buttons in her collection. She will collect 29 new buttons every year. Felicia collects buttons for k years. For what values of k will Felicia have at most 120 buttons?

Write the equation that represents this word problem:

Nicholas received $100 for his birthday. He decides to spend $20 per day on whatever he wants.

• y= 20x + 100

• y= -20x - 100

• y= 20x - 100

• y= -20x + 100

• Answer Not Here

Jackson started with $800 in his savings account, but has to pay $30 a month for his electricity bill. Write an equation that relates his savings, y, to the amount of months, x.

• y = -30x + 800

• y = 30x - 800

• y = -30x

• y = 12x - 30

Which situation is best represented by the following equation? 45w + 123.95 = 753.95

• Erica paid $753.95 for dance classes. She paid a $123.95 registration fee and $45 for each week she was enrolled in the classes. What is w, the number of weeks Erica was enrolled in dance classes?

• Erica paid $753.95 for dance classes. She paid a $45 registration fee and $123.95 for each week she was enrolled in the classes. What is w, the number of weeks Erica was enrolled in dance classes?

• Erica and her sister paid $753.95 for dance classes. Erica paid a $123.95 for each week she was enrolled in the classes, and her sister paid $45 for each week she was enrolled in the classes. What is w, the number of weeks Erica and her sister were enrolled in dance classes?

• Erica paid $753.95 for dance classes. She paid a $123.95 for each week she was enrolled in the classes after using a coupon that gave her $45 off the price per week. What is w, the number of weeks Erica was enrolled in dance classes?

Which situation can be represented by this inequality? 1.25x - 6.50 > 50

• Stefan spends $6.50 on supplies for a lemonade stand and sells each cup of lemonade for $1.25. What is x, the number of cups of lemonade Stefan must sell to earn a profit of more than $50?

• Stefan spends $1.25 on supplies for a lemonade stand and sells each cup of lemonade for $6.50. What is x, the number of cups of lemonade Stefan must sell to earn a profit of more than $50?

• Stefan spends $6.50 on supplies for a lemonade stand and sells each cup of lemonade for $1.25. What is x, the number of cups of lemonade Stefan must sell to earn a profit of at least $50?

• Stefan spends $1.25 on supplies for a lemonade stand and sells each cup of lemonade for $6.50. What is x, the number of cups of lemonade Stefan must sell to earn a profit of at least $50?