Linear Inequalities Word Problems and Graphs

A donut shop charges $0.70 for each donut and $0.30 for a carryout box.  Shirley has $5.00 to spend.  She needs to determine the most donuts (x) she can buy when she only puts them in one carryout box.  Which equation can be used to answer this problem?

• 70x + 30 < 500

• 30x + 70 < 500

• 70x + 30 ≤500

• 30x + 70 ≤ 500

At the Big Bear video rental store, blank CDs cost $1.50 each and blank DVDs cost $3.25 each.  Which of the following statements best describes the number of CDs (c) and DVDs (d) that can be purchased for less than $65.00?

• 150c + 325d < 6,500

• 325c + 150d <6,500

• 150c + 325d ≤ 6,500

• 325c + 150d ≤ 6,500

greater than less than less than or equal to greater than or equal to

• greater than

• less than

• less than or equal to

• greater than or equal to

Q1. What is the comparison operator that checks if one value is greater than another?

• greater than

• less than

• less than or equal to

• greater than or equal to

At the end of the day, vegetables at the farmer’s market sells for $3.00 a pound, and a basket costs $5.50. If Carol wants to buy a basket and spend no more than $10.00 total, how many pounds of vegetables can she buy?

• 3 + 5.5p < 10

• 20 = 5.5 - 3p

• 5.5 + 3p < 20

• 3p + 5.5 ≤20

A willow tree is 5.1 feet tall and grows at a rate of 2.5 feet a year. After how many years will the tree have reached no more than 60 feet tall?

• 5.1 + 2.5y ≥ 60

• 60 < 5.1 + 2.5

• 5.1 + 2.5y ≤ 60

• 5.1 + 2.5y > 60

Mona is ordering cups for her school.  Company A charges $3.50 for each cup and a one-time starter fee of $14.  Company B charges $0.50 for each trophy and a one-time starter fee of $22.  
Which inequality can be used to find x, the minimum number of cups that can be ordereed so that the total charge at Company A is less than the total charge at Company B?

• 3.5x + 14 < 0.5x + 22

• 3.5x + 14 > 0.5x + 22

• 3.5 + 14x < 0.5 + 22x

• 3.5 + 14x > 0.5 + 22x

Four times a number increased by  7 is at least 19. 

• 4x > 19

• 4x + 7 ≥ 19

• 4x < 19

• 4x + 7 ≤ 19

Ross and Chandler go to Taco Land and order sodas for a total of $3.50. They also want to order some tacos (of course), which cost $1.75 each. If they have $20, how many tacos can they buy? Which inequality best represents the situation.

• 3.50 + 1.75t > 20

• 1.75 + 3.50t ≤ 20

• 3.50 + 1.75t ≥ 20

• 1.75t + 3.50 ≤ 20

Erin can read at least 80 words per minute. Write an inequality to show this situation. 

• x > 80

• x < 80

• x ≥ 80

• x ≤ 80