Two Step Inequalities from Words

A cleaning service offers its customers a choice between the two plans.  
-Plan A costs $3000 and includes 1 year of unlimited cleanings
-Plan B costs $75 per cleaning
Henry wants to choose the less expensive plan.  He uses the inequality 3000<75c to deduce which plan to choose based on the number of cleanings (c) he expects to need.  Based on the solution of this inequality, which statement about Henry's choice of plan is true?

• Henry should choose plan A only if he expects to need fewer than 40 cleanings in 1 year.

• Henry should choose plan A only if he expects to need more than 40 cleanings in 1 year.

• Henry can choose either plan and pat the same amount if he expects to need fewer than 40 cleanings in 1 year.

• Henry can choose either plan and pay the same amount if he expects to need more than 40 cleanings in 1 year.

Kelly is planning a business trip to Hartford, CT and Boston, MA. She is going to stay no more than 5 nights on the trip. She estimates each night she stays at a hotel in Hartford will cost $90, and each night she stays at a hotel in Boston will cost $120. She wants to spend no more than $540 for hotel stays. Which graph represents the possible combinations of nights she can stay in Hartford (x) and nights she can spend in Boston (y)?

• A

• B

• C

• D

A baker makes two types of doughnuts. It costs $0.25 to make each glazed doughnut and $0.30 to make each chocolate doughnut. The baker wants to make more than 200 doughnuts for the day but can spend no more than $60.00 making them. The system of inequalities below describes the relationship between the number of glazed doughnuts (x) and chocolate doughnuts (y) the baker could make for the day.
0.25x+0.30y≤60.00
x+y>200
One solution of the system of inequalities is the ordered pair (100,110). Which statement best describes the meaning of the solution?

• The baker could make 100 glazed doughnuts and 110 chocolate doughnuts

• The baker could earn $100 from glazed doughnuts and $110 from chocolate doughnuts

• The baker can make a maximum of 100 glazed doughnuts and 110 chocolate doughnuts

• The baker will spend exactly $60 making 100 glazed doughnuts and 110 chocolate doughnuts

At most and No more than are both clue words for...

• <

• >

• ≤

• ≥

Pick the correct inequality.

• A

• B

• C

• D

Ruby set a goal of saving at least $200 in a savings account. She currently has $60 in the account. If she invests $5 of her weekly allowance per week, how many weeks will it take her to reach her goal? Write the inequality to the problem.

• 5x+60 ≥ 200

• 5x+60 ≤ 200

• 60x+5 ≥ 200

• 60x+5 ≤ 200

You have $14 in your pocket. A taxi has a ride fee of $5 plus an additional fee of $0.60 per mile. What is the most miles you could ride in the taxi? Write the inequality to the problem.

• 0.60x+5 ≥ 14

• 0.60x+5 ≤ 14

• 0.60x+5 > 14

• 0.60x+5 < 14

Henry has run 20 miles so far this week. If he intends to run more than 50 miles this week, how many miles on average should he run on each of the 2 days remaining in the week?

• 20 + 2x ≤ 50

• 20 - 2x ≤ 50

• 20 + 2x > 50

• 20 - 2x < 50

Write an inequality:
Twenty-two more than four times a number is less than 82.

• 22 + 4n ≤ 82

• 22 + 4n > 82

• 82 + 22n ≥ 4

• 22 + 4n < 82

Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.65 per mile.  Katie has no more than $10 to spend on the taxi ride.

• 1.75 + 0.65m < 10

• 1.75 + 0.65m > 10

• 1.75m + 0.65 < 10

• 1.75m + 0.65 > 10