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1 SOLVING WORD PROBLEMS WITH EQUATIONS OF ONE DEGREE AND ONE UNKNOWN Some general “vocabulary” for translating words to mathematical symbols Words that translate into “equals” (=) IS; WILL BE; ARE; EQUALS; RESULT; YIELDS; COSTS; AMOUNTS Words that translate into “multiplication” ( × ) PRODUCT; TIMES; OF; BY; MULTIPLIED BY Words that translate into “division” ( ÷ ) RATIO; QUOTIENT; “TO” Words that translate into “addition” (+) SUM; TOTAL; INCREASED BY; MORE; GREATER THAN; LARGER THAN Words that translate into “subtraction” (-) DIFFERENCE; THE DIFFERENCE BETWEEN; DECREASED BY; LESS; SMALLER; FEWER THAN EXAMPLES 1. Two-thirds of X decreased by one-third is twenty-five. 42 = 3 1 - x 3 2 2. Fifteen is six less than twice the X value. 15 = 2X – 6 3. Jim’s age is 15 less than his mother's is. J = M – 15 4. Twice the sum of two quantities amounts to 42. 2(M + N) = 42 Steps to follow in solving word problems Read the entire problem carefully to get an over-all view. 1. From wording ad given facts, identify the type of problem (i.e. mixture, work, distance, etc.) 2. Set up the guiding structure (i.e. chart, diagram, table) used for this type of problem. 3. Go back to problem; reread it; identify specifically what you are asked to find. a) If you are being asked to find ONE thing, call this quantity “x.” b) If you are being asked to find more than one thing, let “X” designate the one you know the least about, OR let “X” designate either one of the unknown if you know about them. c) If you do not mind dealing with the system of equations let the other variable be equal to “Y”, but remember the objective in this section is to solve word problems using one equation and one unknown. If you decide to choose only one variable, express the other unknowns in terms of “X” using information
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2 given in the problem. Note: Letters always represent measurements or quantities about people and things; they do not represent people or things. 4. Fill in the chart, table or diagram using the given information for the “X”, the other quantity in terms of “X”. Certain memorized formulas (known math formula such as D = RT, I = PRT, etc. are very useful. 5. Using the completed chart and the other relationship information in the problem set up an equation and solve it for X. 6. Go back to the problem and answer the question asked. Note: There is no absolute law about the best way to solve word problems. These outlined procedures have been found helpful by many students because they provide clear-cut ways to get at the information and use it to solve the problem. If you prefer to use intuition or trial and error (which are always good in mathematics, but sometimes inefficient), you may certainly do so. Now, try the above steps in the following problems. NUMBER PROBLEM ADDITIONAL HINTS FOR NUMBER PROBLEMS Consecutive integers can be represented by N, N+1, N+2 , etc. Consecutive odd or even integers can be represented by N, N+2, N+4, etc. The square of the number N is N 2; the cube of the number N is N 3 EXAMPLE 1. Find two numbers whose sum is 18 if one number is 8 more than the other.
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This note was uploaded on 12/13/2010 for the course GM 400 taught by Professor - during the Spring '10 term at Keller Graduate School of Management.

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