4. Linear inequality word problems[1].docx

Linear inequality word problems 1. The following function gives the amount of money owed on a short term loan after t weeks. A(t)=100⋅1.2512 Which numerical expression best approximates the annual interest rate, excluding any late fees? (1 year=52 weeks.) A. 1-0.2526 B. 0.2526-1 C. 26·0.25 D. 26 · 1.25 Correct answer: B Difficulty level: 2 2. The rabbit population in an isolated forest rises and falls depending on the population of predators. Within the year 2014, the population, p, in thousands of rabbits mmm months after January 1, 2014 is: p=0.05(m−1.5)(m−8.5)+10 The population reached ten thousand some time in February. At what other time, given as months after January 1, 2014, did the rabbit population reach ten thousand? Correct answer: 8.5 Difficulty level: 2 3. The "hang time" of a football is the amount of time the football stays in the air after being kicked. The height, in meters, of the football above the ground at time t can be modeled by the quadratic function: ht=-4.9t2+19.6t Which of the following equivalent expressions displays the hang time of the football as a constant or coefficient? A. -4.9(t-2)2+19.6 B. -4.9t(t-4) C. -4.9t-32-9.8t+44.1 D. -4.9t-12+9.8t+4.9 Correct answer: B Difficulty level: 2 4. Kaia throws a stone vertically upward from a bridge. The height, in meters, of the stone above the water at time t can be modeled by the quadratic function: h(t)=-4.9t2+9.8t+39.2 After how many seconds does the stone hit the water? A. 1 second B. 2 seconds C. 4 seconds D. 8 seconds Correct answer: C Difficulty level: 2 5. More than 450 students traveled to a state park for a field trip. The school allowed 6 students to travel by car, and the rest traveled on 11 buses, each of which held the same number of students. If there were s students in each bus, which inequality best represents this situation? A. 11s+6>450 B. 11s+6<450 C. 6s+11>450 D. 6s+11<450 Correct answer: A Difficulty level: 2 6. A barber charges $12 for a haircut. His operating expenses are, on average, $37 per day. He calculates his profit by subtracting his operating costs from the money he earns from the haircuts he gives. In a given day, the barber expects to make a profit of at least $86. If the barber gives h haircuts in a day, which inequality best models this situation? A. 12h-37≥86 B. 12(h-37)≥86 C. 12h+37≥86 D. 12(h+37)≥86 Correct answer: A Difficulty level: 2 7. A distributor ships DVDs to several stores. The shipping boxes contain several DVDs (in their cases) plus a layer of padding at each end of the box. The DVD cases and layers of padding can be arranged neatly inside each box. Each DVD case is 14 mm (millimeters) thick, each layer of padding is 10 mm thick, and the length of the interior of the box is 132 mm. If d represents the number of DVDs that the distributor can fit into one box with two layers of padding, which of the following inequalities best models the situation? A. 10d+14≤132 B. 14d+20≤132 C. 20d+14≤132 D. 14d+10≤132 Correct answer: B Difficulty level: 2 8. To rent a car for one week, a car rental company charges a $200 base price as well as $0.45 per mile. Jennifer will rent a vehicle at this company, but she has a $275 budget. Which of the following is a possible number of miles that Jennifer can drive without exceeding her budget? A. 166 miles B. 167 miles C. 168 miles D. 169 miles Correct answer: A Difficulty level: 2 9. Woo-Jin would like to bring several books from his favorite series in his backpack. The backpack can hold up to a depth of 1012 inches of materials. Woo-Jin's laptop and a notebook fill a total of 3 inches of that depth. Each book would fill 1.5 inches of the depth of the backpack. Only one stack of books can fit the height and width of the backpack. If x represents the number of books that Woo-Jin could carry in his backpack, which of the following inequalities best models the situation described above? A. 3+1.5x<10.5 B. 3+1.5x≤10.5 C. 3x+1.5<10.5 D. 3x+1.5≤10.5 Correct answer: B Difficulty level: 2 10. In the year 2000, the average American consumed 8.3 gallons of whole milk per year. This amount has been decreasing by 0.3 gallons per year. Which inequality can be used to find the number of years, t, since 2000 when whole milk consumption was greater than 6.0 gallons per person per year? A. 8.3-0.3t>6.0 B. 8.3-0.3(t-2000)>6.0 C. 8.3-0.3t<6.0 D. 8.3-0.3(t-2000)<6.0 Correct answer: A Difficulty level: 3 11. An amusement center charges a $45 flat fee for any birthday party plus $3.50 for each guest after the first one. Josiah wants to spend no more than $200 for his birthday party. If there are x guests, which of the following inequalities best models the situation above? A. 45+3.50x≤200 B. 45+3.50(x-1)≤200 C. 45x+3.50≤200 D. 45x-1+3.50≤200 Correct answer: B Difficulty level: 3 12. Hamadi is renting a car. With his extreme coupons, the rental charge is $17.50 per day plus $0.16 per mile. His company will reimburse Hamadi for $33 of this portion of the travel expenses. If he rents the car for one day, what is one possible number of miles paid for by the company? A. 53 B. 97 C. 110 D. 150 Correct answer: A Difficulty level: 3 13. To get to school, Da'Quon walks 0.6 miles from his house to the bus stop. He then takes the bus for 3.9 miles. After he gets off the bus, he can choose one of several walking routes to school. The total amount of miles he travels, via walking and bus, does not exceed 5.4. What is the greatest possible number of miles he walks after getting off the bus? A. 0.0 miles B. 0.3 miles C. 0.9 miles D. 1.5 miles Correct answer: C Difficulty level: 3 14. Karim has a $35 gift card to his favorite restaurant. Meal tax in his area is 14.3%. Karim would also like to leave a $5 tip. If c represents Karim's pre-tax bill, and he wants to pay the entire meal amount, including tip and tax, using the gift card, which of the following inequalities best models the situation described above? A. 1.143c-5≥35 B. 1.143c+5≤35 C. 0.143c-5≤35 D. 0.143c+5≥35 Correct answer: B Difficulty level: 3 15. One of the rules in a public speaking contest requires contestants to speak for as close to 3 minutes (180 seconds) as possible. Contestants lose 2 points for each second they speak either over or under the 3 minutes. If a contestant lost 18 points, what are the possible lengths of time they spoke? A. 171 and 186 seconds B. 174 and 186 seconds C. 171 and 189 seconds D. 174 and 189 seconds Correct answer: C Difficulty level: 1 16. A gemologist determines that a gemstone weighs 1.235 carats. Guidelines allow a maximum weighing error of 0.001 carats in reporting gemstone weight. Which of the following equations can be used to determine the smallest and largest possible true weights, c, of the gemstone? A. |c-0.001|=1.235 B. |c-1.235|=0.1235 C. |c-0.001|=0.01 D. |c-1.235|=0.001 Correct answer: D Difficulty level: 1 17. A company's unit cost for producing x units is a minimum when x=2,000 units are produced. The unit cost increases $0.25 for every unit more or less than 2,000 produced. Which of the following could be the number of units for which the unit cost increases by $7.50 from the minimum? A. 1,700 or 2,300 B. 1,975 or 2,025 C. 1,997 or 2,003 D. 1,970 or 2,030 Correct answer: D Difficulty level: 1 18. Felipe has a 15 gallon gas tank in his car. He fills his tank, and then drives the x miles back to college. Upon his arrival, he fills his tank for $20.91. If his car averages 24 miles per gallon (mpg), and at the time, gas costs $2.46 per gallon, which of the following best approximates x? A. 128 B. 204 C. 360 D. 502 Correct answer: B Difficulty level: 1 19. In 2005, approximately 16.5% of seats in national parliaments were held by women. Between 2005 and 2014, this percentage increased at a constant rate of about 3 percentage points every 5 years. If t is the year when approximately 19% of the seats in national parliaments were held by women, which of the following equations best models the situation? A. 16.5+3t=19 B. 16.5+35t=19 C. 16.5+3(t-2005)=19 D. 16.5+35(t-2005)=19 Correct answer: D Difficulty level: 1 20. Ella needs a 70% isopropyl alcohol solution as an antiseptic. She has a 100 milliliter (ml) container of 90% isopropyl alcohol solution. Approximately how much water should Ella add to dilute it to a 70% isopropyl alcohol solution? Round to the nearest tenth. ml of water Correct answer: 28.6 Difficulty level: 1 21. For many trees, the approximate age of the tree (in years) is equal to the diameter of the tree (in inches) times the tree's growth factor. Deniz estimates that a certain red maple tree in her yard is about 80 years old. If red maple trees have a growth factor of 4.5, which of the following equations could be used to find x, the diameter of the tree in feet? A. 80=12(4.5x) B. 80=4.5x12 C. 80=12x4.5 D. 80=x(12)(4.5) Correct answer: A Difficulty level: 1 22. The property taxes in a town decrease as the distance from the town hall increases. For every 5 miles from the town hall, property taxes decrease by 0.2 percentage points. Which of the following equations can be used to determine how far north or south of the town hall a house is whose property taxes are 0.76 percentage points less than the taxes at the town hall? Note: y is the position of a house that is directly north or south of the town hall, with y>0 representing north and y<0 representing south. A. 0.04|y-5|=0.76 B. 0.04|y|=0.76 C. 4|y-5|=0.76 D. 4|y|=0.76 Correct answer: B Difficulty level: 1 23. Josie's hair currently falls about 16 centimeters (cm) below her shoulder and grows about 5 cm every 4 months. Josie plans to grow her hair and donate about 21 cm of her hair to charity after her next haircut. If Josie would like to have her hair fall about 5 cm below her shoulders after her next haircut, which of the following equations could be used to find the number of months, mmm, for which Josie must grow her hair? A. 1.25m=5 B. 1.25m=21 C. 16+1.25m-21=5 D. 5+1.25m-16=21 Correct answer: C Difficulty level: 1 24. Melissa has an 80 inch (in) piece of wrought iron that she wishes to use to make a rectangular piece of art. She wants the length of the rectangular piece of art to be 12 inches longer than the width. What is the largest length possible? A. 14 in B. 26 in C. 34 in D. 46 in Correct answer: B Difficulty level: 1 25. Yong needs to cut a 3 foot long board into several 2 inch lengths. With each cut, his saw blade shaves off an additional 18 inch of the board. What is the maximum number of full 2 inch lengths that Yong can cut from his board? lengths Correct answer: 17 Difficulty level: 1 26. Aria is buying refreshments for a birthday party. She intends to get an ice cream cake for $23 and some cupcakes for $2 each. Aria has a $45 budget but does not have to spend the entire amount. Which inequality best represents the number of cupcakes, c, that Aria can purchase? A. c>11 B. c<11 C. c≥11 D. c≤11 Correct answer: D Difficulty level: 2 27. Stan is crocheting scarves to sell at a craft fair. He will give away the first 2 scarves that he crochets and will sell the rest at the craft fair for $8 each. His scarves are very popular and people always buy all that he is willing to sell. Stan's goal is to earn at least $75 at the craft fair. If n represents the number of scarves which Stan needs to crochet to meet his goal, which of the following inequalities best models the situation described above? A. 8n-2≥75 B. 8n≥75-2 C. 8(n-2)≥75 D. (8-2)n≥75 Correct answer: C Difficulty level: 2 28. In golf, someone who completes a course in fewer strokes beats someone who completes it with more strokes. Par means the standard number of strokes it takes to complete a specific course. Amateurs generally require more strokes. Ayumi averages 1.5 times par strokes per game, but her brother Daiki averages 1.75 times par strokes per game. To make the game more even, Ayumi adds 18 strokes to her total when she plays against Daiki. Assuming both Ayumi and Daiki play average games, which inequality best represents the par, p, in a golf game where Ayumi beats her brother Daiki? A. p>41 B. p>54 C. p>72 D. p>90 Correct answer: C Difficulty level: 2 29. Arianna and Hannah are conducting an experiment to test the difference threshold for sense of touch on the forehead. For trial 1, Hannah closes her eyes while Arianna gently touches 2 paperclip points 3 millimeters (mm) apart on Hannah's forehead. Then Hannah reports whether she could feel 1 or 2 points. For each of the next trials, Arianna and Hannah repeat this process, each time with the points 2 more mm apart. Hannah reports feeling 1 point until the points are 15mm apart, when she begins reporting that she feels 2 points. Which inequality best represents the trial numbers in which Hannah feels 2 points? A. t>6 B. t<6 C. t≥7 D. t≤7 Correct answer: C Difficulty level: 2 30. Turkey's government requires at least a 23 majority of Parliament members to approve any constitutional changes. There are 550 seats in the Parliament. Of those, 313 of the seats are occupied by members who have pledged to support a particular constitutional change. Which inequality represents the number of additional Parliament members, m, who would need to support the constitutional change to achieve the required majority? A. m≥53.6 B. m≥158 C. m≥303 D. m≥366.6 Correct answer: A Difficulty level: 2 31. In one state, a minimum of 246,400 valid signatures on a petition is required to get a voter initiative added to a state-wide ballot. The signature collectors can fit 25 signatures per page. They estimate that 61,600 of the signatures that they collect will not be valid (because of being duplicates, incomplete, or unregistered voters). If p represents the number of pages of signatures which the signature collectors should collect in order to get the voter initiative added to the ballot, which of the following inequalities best models the situation described above? A. 25p+61,600≥246,400 B. 25p+61,600≤246,400 C. 25p-61,600≥246,400 D. 25p-61,600≤246,400 Correct answer: C Difficulty level: 2 32. When police analyze the broken glass at a scene, it helps them reconstruct the situation. Headlight glass is much less dense than the window glass. The headlight glass will be 1.5 grams per milliliter or less. A police officer determines that a fragment of glass displaces 10.5mLof water. Use the formula density=massvolume. Which inequality best shows the possible mass, m, in grams of the fragment if it is headlight glass? A. m≥7 B. m≤7 C. m≥15.75 D. m≤15.75 Correct answer: D Difficulty level: 2 33. Jennifer wants to spend no more than $300 on school clothes. She spends $75