Algebra Word Problems

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NAME ______________________________________________ DATE______________ PERIOD _____ 1-1 Word Problem Practice Variables and Expressions BLOCKS For Exercises 5–7, use the following information. A toy manufacturer produces a set of blocks that can be used by children to build play structures. The product packaging team is analyzing different arrangements for packaging their blocks. One idea they have is to arrange the blocks in the shape of a cube, with b blocks along one edge. 1. SOLAR SYSTEM
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  Chapter 1 10 Glencoe Algebra 1 1. SOLAR SYSTEM It takes Earth about365 days to orbit the sun.It takesUranus about 85 times as long.Write anumerical expression to describe thenumber of days it takes Uranus to orbitthe sun. 2. TECHNOLOGY There are 1024 bytes ina kilobyte.Write an expression thatdescribes the number of bytes in acomputer chip with n kilobytes. 3. THEATER Howard Hughes,ProfessorEmeritus of Texas Wesleyan College,reportedly attended a record 6136theatrical shows.Write an expression torepresent the average number of theatershows attended if he accumulated therecord over  y years.Use the expression tofind the average number of shows Mr.Hughes attended per year if he went tothe theater for 31 years. 4. TIDES The difference between high andlow tides along the Maine coast inNovember is 19 feet on Monday and  x feet on Tuesday.Write an expression toshow the average rise and fall of the tidefor Monday and Tuesday. BLOCKS For Exercises 5–7,use thefollowing information.  A toy manufacturer produces a set of blocksthat can be used by children to build playstructures.The product packaging team isanalyzing different arrangements forpackaging their blocks.One idea they haveis to arrange the blocks in the shape of acube,with b blocks along one edge. 5. Write an expression representing thetotal number of blocks packaged in acube measuring b blocks on one edge. 6. The packaging team decides to take onelayer of blocks off the top of this package.Write an expression representing thenumber of blocks in the top layer of thepackage. 7. The team finally decides that theirfavorite package arrangement is to take2 layers of blocks off the top of a cubemeasuring b blocks along one edge.Writean expression representing the numberof blocks left behind after the top twolayers are removed. WordProblem Practice Variables and Expressions  NAME ______________________________________________ DATE______________ PERIOD _____  1-1  C  o p y r i   gh  t   © Gl   en c  o e /  M c  Gr  aw-H i  l  l   , a d i  v i   s i   on of  T h  eM c  Gr  aw-H i  l  l   C  om p ani   e s  ,I  n c . b b b   Word Problem Practice Order of Operations  NAME ______________________________________________ DATE______________ PERIOD _____  1-2 1-2 Chapter 1 17 Glencoe Algebra 1    L  e  s  s  o  n    1  -   2 1. SCHOOLS Jefferson High School has100 less than 5 times as many studentsas Taft High School.Write and evaluatean expression to find the number of students at Jefferson High School if TaftHigh School has 300 students. 2. GEOGRAPHY Guadalupe Peak in Texashas an altitude that is 671 feet morethan double the altitude of MountSunflower in Kansas.Write and evaluatean expression for the altitude of Guadalupe Peak if Mount Sunflower hasan altitude of 4039 feet. 3. TRANSPORTATION The Plaid Taxi CabCompany charges $1.75 per passengerplus $3.45 per mile for trips less than 10miles.Write and evaluate an expressionto find the cost for Max to take a Plaidtaxi 8 miles to the airport. 4. GEOMETRY The area of a circle isrelated to the radius of the circle suchthat the product of the square of theradius and a number  gives the area.Write and evaluate an expression for thearea of a circular pizza below. Approximate  as 3.14. 5. BIOLOGY Lavania is studying thegrowth of a population of fruit flies inher laboratory.She notices that thenumber of fruit flies in her experiment isfive times as large after any six-dayperiod.She observes 20 fruit flies onOctober 1.Write and evaluate anexpression to predict the population of fruit flies Lavania will observe onOctober 31. CONSUMER SPENDING For Exercises6–8,use the following information. During a long weekend,Devon paid a totalof  x dollars for a rental car so he could visithis family.He rented the car for 4 days at arate of $36 per day.There was an additionalcharge of $0.20 per mile after the first 200miles driven. 6. Write an algebraic expression torepresent the amount Devon paid foradditional mileage only. 7. Write an algebraic expression torepresent the number of miles over 200miles that Devon drove the rented car. 8. How many miles did Devon drive overallif he paid a total of $174 for the carrental?    C  o  p  y  r   i  g   h   t   ©   G   l  e  n  c  o  e   /   M  c   G  r  a  w  -   H   i   l   l ,  a   d   i  v   i  s   i  o  n  o   f   T   h  e   M  c   G  r  a  w  -   H   i   l   l   C  o  m  p  a  n   i  e  s ,   I  n  c . 7 in.  Word Problem Practice Open Sentences  1 -3 Chapter 1 25 Glencoe Algebra 1    L  e  s  s  o  n    1  -   3    C  o  p  y  r   i  g   h   t   ©   G   l  e  n  c  o  e   /   M  c   G  r  a  w  -   H   i   l   l ,  a   d   i  v   i  s   i  o  n  o   f   T   h  e   M  c   G  r  a  w  -   H   i   l   l   C  o  m  p  a  n   i  e  s ,   I  n  c . 1. TIME There are 6 time zones in theUnited States.The eastern part of theU.S.,including New York City,is in theEastern Time Zone.The central part of the U.S.,including Dallas,is in theCentral Time Zone,which is one hourbehind Eastern Time.San Diego is in thePacific Time Zone,which is 3 hoursbehind Eastern Time.Write and solve anequation to determine what time it is inCalifornia if it is noon in New York. 2. FOOD Part of the Nutrition Facts labelfrom a box of macaroni and cheese isshown below.Write and solve an inequality todetermine how many servings of thisitem that Alisa can have for lunch if sheis restricted no more than 45 grams of cholesterol. 3. CRAFTS  You need at least 30 yards of yarn to crochet a small scarf.Cherylbought a 100-yard ball of yarn and hasalready used 10 yards.Write and solvean inequality to find how many scarvesshe can crochet. 4. POOLS There are approximately 202gallons per cubic yard of water.Writeand solve an equation for the number of gallons of water that fill a pool with a volume of 1161 cubic feet.(  Hint: Thereare 27 cubic feet per cubic yard.) VEHICLES For Exercises 5 and 6,use thefollowing information. Recently developed hybrid cars contain bothan electric and a gasoline engine.Hybrid carbatteries store extra energy,such as theenergy produced by braking.Since the carcan use this stored energy to power the car,the hybrid uses less gasoline per mile thancars powered only by gasoline.Suppose anew hybrid car is rated to drive 45 miles pergallon of gasoline. 5. It costs $40 to fill the gasoline tank withgas that costs $2.50 per gallon.Write andsolve an equation to find the distance thehybrid car can go using one tank of gas. 6. Write and solve an equation to find thecost of gasoline per mile for this hybridcar.Round to the nearest cent. Nutrition Facts Serving Size 1 cup (228g)Servings Per Container 2 Amount Per Serving Calories 250Calories from Fat 110 Total Fat 12gSaturated Fat 3g Trans  Fat 3g Cholesterol 30mg % Daily Value *18 %15 %10 %   1-3 NAME ______________________________________________ DATE______________ PERIOD _____   Word Problem Practice Identity and Equality Properties  1 -4 1-4 Chapter 1 33 Glencoe Algebra 1    L  e  s  s  o  n    1  -   4 1. EXERCISE  Annika goes on a walk everyday in order to get the exercise herdoctor recommends.If she walks at arate of 3 miles per hour for  13  of an hour,then she will have walked 3   13  miles.Evaluate the expression and name theproperty used. 2. MAIL The chart below shows the cost of mailing letters of various weight throughthe United States Postal Service. USPS First Class Mail:Standard Letter Rates Source: www.usps.gov Write an equation that represents thedifference between the cost of mailing a0.5 ounce and a 1.0 ounce letter.Namethe property illustrated. 3. CAPACITY Use the substitution andtransitive properties to find how many1-cup servings there are in 1 gallon of sports drink. 4. PARTY PLANNING Chase is planning adinner party for 18 guests.He needs tohave the same number of place settingsas guests,and the same number of waterglasses as place settings.What propertymust be used to determine the numberof water glasses he needs for the party?Explain. TOLL ROADS For Exercises 5 and 6,usethe following information. Some toll highways assess tolls based onwhere a car entered and exited.The tablebelow shows the highway tolls for a carentering and exiting at a variety of exits. Assume that the toll for the reversedirection is the same. 5. Running an errand,Julio travels fromExit 8 to Exit 5.What property wouldyou use to determine the toll? 6. Gordon travels from home to work andback each day.He lives at Exit 15 on thetoll road and works at Exit 22.Write andevaluate an expression to find his dailytoll cost.What property or properties didyou use?    C  o  p  y  r   i  g   h   t   ©   G   l  e  n  c  o  e   /   M  c   G  r  a  w  -   H   i   l   l ,  a   d   i  v   i  s   i  o  n  o   f   T   h  e   M  c   G  r  a  w  -   H   i   l   l   C  o  m  p  a  n   i  e  s ,   I  n  c . Weight(ounces)Cost 0.25 $0.390.5 $0.390.75 $0.391 $0.391.25 $0.601.5 $0.601.75 $0.60 EnteredExitedToll Exit 5 Exit 8 $0.50Exit 8 Exit 10 $0.25Exit 10 Exit 15 $1.00Exit 15 Exit 18 $0.50Exit 18 Exit 22 $0.75NAME ______________________________________________ DATE______________ PERIOD _____ 
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