How Do You Know a Problem Is Algebraic

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Yous tin solve many real world problems with the help of math. In gild to familiarize students with these kinds of problems, teachers include word problems in their math curriculum. However, word problems tin nowadays a existent challenge if you don't know how to interruption them downwardly and detect the numbers underneath the story. Solving word problems is an art of transforming the words and sentences into mathematical expressions and then applying conventional algebraic techniques to solve the problem.

1. ane

   Read the problem carefully. ^[1] A common setback when trying to solve algebra word problems is bold what the question is request earlier you read the entire trouble. In order to be successful in solving a discussion trouble, you need to read the whole problem in order to assess what information is provided, and what information is missing.^[2]

2. 2

   Determine what you are asked to notice. In many problems, what you are asked to discover is presented in the last judgement. This is non always true, yet, and so y'all need to read the entire problem advisedly.^[3] Write downward what yous need to observe, or else underline information technology in the problem, then that you practise not forget what your concluding respond means.^[4] In an algebra discussion problem, you volition likely be asked to find a certain value, or you may exist asked to find an equation that represents a value.

   • For example, y'all might accept the following problem: Jane went to a book store and bought a volume. While at the store Jane found a second interesting book and bought it for $80. The price of the second book was $ten less than three times the price of he start book. What was the toll of the get-go book?
   • In this problem, you are asked to find the cost of the offset book Jane purchased.

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3. iii

   Summarize what you know, and what you need to know. Likely, the data yous need to know is the same equally what information you are asked to notice. You as well need to assess what data you lot already know. Again, underline or write out this data, so you can go on track of all the parts of the trouble. For problems involving geometry, information technology is often helpful to describe a sketch at this indicate.^[5]

   • For example, you know that Jane bought two books. You know that the second book was $80. You also know that the second volume cost $x less than 3 times the cost of the first book. You don't know the toll of the first book.

4. 4

   Assign variables to the unknown quantities. If you lot are being asked to find a certain value, you volition likely only have one variable. If, nevertheless, you are asked to find an equation, you will likely have multiple variables. No affair how many variables y'all have, you lot should list each one, and indicate what they are equal to.^[6]

5. 5

   Await for keywords. ^[seven] Word problems are full of keywords that give you clues about what operations to apply. Locating and interpreting these keywords can assistance you translate the words into algebra.

   • Multiplication keywords include times, of, and factor. ^[8]
   • Division keywords include per, out of, and pct. ^[9]
   • Addition keywords include some, more, and together. ^[10]
   • Subtraction keywords include deviation, fewer, and decreased. ^[11]

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1. 1

   Write an equation. Use the data you learn from the problem, including keywords, to write an algebraic description of the story.^[12]

2. 2

   Solve an equation for i variable. If you take simply ane unknown in your word problem, isolate the variable in your equation and observe which number it is equal to. Use the normal rules of algebra to isolate the variable. Think that yous need to proceed the equation counterbalanced. This means that whatever y'all practice to 1 side of the equation, you must as well practice to the other side.

3. iii

   Solve an equation with multiple variables. If you have more one unknown in your discussion trouble, you need to brand sure yous combine like terms to simplify your equation.

4. 4

   Interpret your answer. Look back to your list of variables and unknown information. This will remind you what you were trying to solve. Write a statement indicating what your answer means.

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1. 1

   Solve the following trouble. This problem has more than than one unknown value, so its equation will have multiple variables. This means y'all cannot solve for a specific numerical value of a variable. Instead, you will solve to find an equation that describes a variable.

   • Robyn and Baton run a lemonade stand. They are giving all the coin that they make to a true cat shelter. They will combine their profits from selling lemonade with their tips. They sell cups of lemonade for 75 cents. Their mom and dad have agreed to double any amount they receive in tips. Write an equation that describes the amount of money Robyn and Billy volition give to the shelter.

2. 2

   Read the trouble carefully and determine what you are asked to detect. ^[13] You are asked to notice how much money Robyn and Billy volition requite to the cat shelter.

3. three

   Summarize what you lot know, and what you need to know. You lot know that Robyn and Baton volition make money from selling cups of lemonade and from getting tips. Yous know that they will sell each cup for 75 cents. You lot as well know that their mom and dad volition double the amount they make in tips. You don't know how many cups of lemonade they sell, or how much tip money they become.

4. iv

   Assign variables to the unknown quantities. Since you have three unknowns, y'all will have 3 variables. Permit ${\displaystyle x}$ equal the amount of money they will give to the shelter. Permit ${\displaystyle c}$ equal the number of cups they sell. Allow ${\displaystyle t}$ equal the number of dollars they make in tips.

5. 5

   Look for keywords. Since they will "combine" their profits and tips, you know addition volition be involved. Since their mom and dad volition "double" their tips, you know you need to multiply their tips by a factor of two.

6. 6

   Write an equation. Since you are writing an equation that describes the corporeality of money they will give to the shelter, the variable ${\displaystyle x}$ will be alone on one side of the equation.

7. 7

   Interpret your answer. The variable ${\displaystyle x}$ equals the amount of coin Robyn and Billy will donate to the cat shelter. So, the amount they donate can be establish by multiplying the number of cups of lemonade they sell by .75, and adding this product to the product of their tip coin and 2.

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Add together New Question

• Question

  How practice you lot solve an algebra give-and-take problem?

  

  Daron Cam is an Academic Tutor and the Founder of Bay Surface area Tutors, Inc., a San Francisco Bay Area-based tutoring service that provides tutoring in mathematics, science, and overall academic confidence building. Daron has over eight years of pedagogy math in classrooms and over 9 years of ane-on-1 tutoring feel. He teaches all levels of math including calculus, pre-algebra, algebra I, geometry, and SAT/ACT math prep. Daron holds a BA from the Academy of California, Berkeley and a math teaching credential from St. Mary'southward College.

  

  Academic Tutor

  Skillful Reply

  Carefully read the problem and figure out what information you're given and what that information should be used for. Once you know what y'all need to do with the values they've given y'all, the trouble should be a lot easier to solve.

• Question

  If Deborah and Colin take $150 between them, and Deborah has $27 more than Colin, how much money does Deborah accept?

  

  Let x = Deborah's money. Then (x - 27) = Colin's money. That ways that (x) + (10 - 27) = 150. Combining terms: 2x - 27 = 150. Adding 27 to both sides: 2x = 177. Then x = 88.50, and (10 - 27) = 61.fifty. Deborah has $88.50, and Colin has $61.l, which together add together up to $150.

• Question

  Karl is twice equally old Bob. Nine years ago, Karl was iii times as old as Bob. How old is each now?

  

  Permit 10 be Bob's current age. Then Karl's electric current age is 2x. 9 years agone Bob'southward age was x-9, and Karl'south age was 2x-9. We're told that 9 years ago Karl's age (2x-9) was 3 times Bob'southward historic period (x-9). Therefore, 2x-9 = iii(x-ix) = 3x-27. Subtract 2x from both sides, and add 27 to both sides: 18 = x. So Bob's electric current age is 18, and Karl's current historic period is 36, twice Bob's current age. (9 years ago Bob would have been ix, and Karl would take been 27, or three times Bob's historic period then.)

• Question

  The pinnacle of a triangle is 4 inches more than than twice the length of the base. The area of the triangle is 35m^ii square inches. What is the height of the triangle?

  

  Allow b equal the length of the base of operations. Then the top is (2b + 4). The expanse is 35 = [(b)(2b + four)] / 2 = [2b² + 4b] / 2 = b² + 2b. So b² + 2b -35 = 0. So (b +7)(b - 5) = 0. That ways b = -7 or five. The length of the base cannot be a negative number, and then the base is 5 inches. That makes the height fourteen inches. (To bank check the answer: [(v)(14)]/2 = 70/2 = 35.)

• Question

  What is 20% of xxx?

  

  (.two)(30) = six.

• Question

  What number is 15 percent of 20?

  

  (.15)(twenty) = 3.

• Question

  How do I write an equation that calculates how many hours someone needs to apply tennis courts to justify becoming a member if the gym charges not-members $10 per hour to apply the courts and members pay a yearly fee of $300 plus $4 per hour to use the courts?

  

  A expert approach is to prepare two equations: Northward(t) = ($10/hour)*t is the annual price to a nonmember who uses a court for an unknown time (t) and M(t) = $300 + ($four/hr)*t is the corresponding toll function for members. You want to solve 1000(t) < N(t) for t so, $300 + ($4/60 minutes)*t < ($ten/hr)*t becomes $300 < ($10/hr)t - ($four/60 minutes)t becomes $300 < ($6/hr)t becomes $300/($6/hr) < t finally becomes 50 hours < t. So 50 hours is the break even indicate where both members and nonmembers pay $500, any college and members pay less.

• Question

  Steve and Josephine run a total of 42 miles in a week. Steve ran 6 fewer miles than Josephine. How many miles did Josephine run?

  

  Permit x be the number of miles Josephine ran. Then (x-six) is the number of miles Steve ran. Their total, 42, can exist represented by ten + (x-half dozen). So x + (x-6) = 2x - vi = 42. Add 6 to both sides: 2x = 48, and x = 24.

• Question

  How would I share £850.00 among 3 people so that the first one gets £50.00 more than the 2d one, and the second gets £100.00 more than the last?

  

  Let x be the starting time share. Then (ten - fifty) is the second share, and (x - 50 - 100) or (10 - 150) is the last share. Add them together: (x) + (x - 50) + (10 - 150) = 3x - 200 = 850. Solve for x by adding 200 to both sides and then dividing both sides by iii: 10 = £350.00. (To check the reply: 350 + 300 + 200 = 850.)

• Question

  2 lighthouse beacons commencement flashing the aforementioned fourth dimension. One flashes once every 4 minutes, and the other flashes one time every ix minutes. How long will it be before they both flash at the aforementioned fourth dimension?

  

  The first fourth dimension they will flash together is 4 ten 9 = 36 minutes afterwards they begin rotating. 36 is the lowest multiple of four that is too a multiple of 9.

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• Word problems can accept more than one unknown and more the i variable.

• While solving word issues you should always read every judgement carefully and effort to extract all the numerical data.

• To gain experience with word bug you should practise as much as yous can.

• The number of variables is always equal to the number of unknowns.

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Article Summary X

To solve word problems in algebra, kickoff by reading the trouble carefully and determining what yous're being asked to find. Next, summarize what information yous know and what you need to know. So, assign variables to the unknown quantities. For example, if you lot know that Jane bought 2 books, and the second book cost $80, which was $10 less than 3 times the toll of the first book, assign ten to the price of the 1st book. Apply this information to write your equation, which is lxxx = 3x - x. To learn how to solve an equation with multiple variables, keep reading!

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Source: https://www.wikihow.com/Solve-Word-Problems-in-Algebra

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