Problem Solving Using Problem Solving Using EquationsEquations

Math word problems can, in most Math word problems can, in most instances, be translated in math equations instances, be translated in math equations and quickly solved.and quickly solved.

The language of math is similar to any The language of math is similar to any other language, complete with nouns, other language, complete with nouns, verbs, adjectives, phrases, sentences verbs, adjectives, phrases, sentences etc…etc…

Problem Solving using EquationsProblem Solving using Equations

A list of some of the symbols, phrases, A list of some of the symbols, phrases, and sentences that you will be using are and sentences that you will be using are listed below to assist you in translating listed below to assist you in translating from English to math and vice versa.from English to math and vice versa.

TranslationTranslation

MathMath English equivalentEnglish equivalent

++ Plus, add, increase, greater than, larger, Plus, add, increase, greater than, larger, augmentaugment

-- Subtract, minus, negative, decrease,less Subtract, minus, negative, decrease,less than,reduce,diminishthan,reduce,diminish

xx Times, of, multiplyTimes, of, multiply

÷÷ Divided, goes into, a certain number of Divided, goes into, a certain number of partsparts

X,a,q,t,p,y,z,n,d,g,m,etc.X,a,q,t,p,y,z,n,d,g,m,etc. A number, an age, a quantity, a mass, a A number, an age, a quantity, a mass, a volume, a certain amount, etc…volume, a certain amount, etc…

7x7x Seven times a number, a number times 7Seven times a number, a number times 7

N+6N+6 A number increased by 6, 6 larger than a A number increased by 6, 6 larger than a numbernumber

T-9T-9 A number decreased by 9, 9 less than a A number decreased by 9, 9 less than a number, a number reduced by 9number, a number reduced by 9

4x+_7=84x+_7=8 4 times a number plus 7 equals 84 times a number plus 7 equals 8

(x)(x) (x)(x) A number times itselfA number times itself

Please Translate TogetherPlease Translate Together

3x3x(3g)(23)(3g)(23)A numberA numberA number doubledA number doubledThe square of a numberThe square of a numberA number increased by fiveA number increased by fiveThe sum of a number and fifteenThe sum of a number and fifteenOne-half of a number plus the numberOne-half of a number plus the numberSix decreased by a number is the numberSix decreased by a number is the numberFive times a number plus eight is eighty-fiveFive times a number plus eight is eighty-fiveThree consecutive numbersThree consecutive numbers

AnswersAnswers

Three times a numberThree times a numberThree times a number times 23Three times a number times 23X , y, r, etc…X , y, r, etc…2x2xXXX+5X+5X=15X=15½ x + x½ x + x 6-x=x6-x=x5x+8=855x+8=85X, x+1, x+2X, x+1, x+2

Try some on your ownTry some on your ownA number is doubled the result is twelveA number is doubled the result is twelveSeven times a number is negative fifty-sixSeven times a number is negative fifty-sixA number plus twice a number plus three times a A number plus twice a number plus three times a number is seventy-fivenumber is seventy-fiveSix less than triple a number is nineSix less than triple a number is nineThe product of five more than a number and six is thirtyThe product of five more than a number and six is thirtyWe get four when we subtract fifteen from twice a We get four when we subtract fifteen from twice a numbernumberThe product of two consecutive numbers is fifty-sixThe product of two consecutive numbers is fifty-sixNine times a number plus the number quadrupled is zeroNine times a number plus the number quadrupled is zero

Putting this Together to Solve Word Putting this Together to Solve Word ProblemsProblems

Example:Example: If a number is doubled and the result is If a number is doubled and the result is

increased by 4, the sum is ninety four. Find the increased by 4, the sum is ninety four. Find the number.number.

2x+4= 942x+4= 942x + 4-4=94-42x + 4-4=94-42x=902x=902x 2x = = 909022 22X= 45X= 45

Problem Solving (Continued)Problem Solving (Continued)

The larger of two numbers is seven more than five times the The larger of two numbers is seven more than five times the smaller. Their sum is sixty-one. What are the numbers?smaller. Their sum is sixty-one. What are the numbers?

Larger: 5x+7 Smaller: xLarger: 5x+7 Smaller: x

5x+7+x=615x+7+x=615x+x=61-75x+x=61-76x=546x=546x 6x = = 545466 66X= 9X= 9

Therefore the smaller number is 9 and the larger is 52 because Therefore the smaller number is 9 and the larger is 52 because 5(9)+7=52 5(9)+7=52

Still more…Still more…

If three is added to a number and the sum is If three is added to a number and the sum is multiplied by two, the result is the same as nine multiplied by two, the result is the same as nine subtracted from three times the number. Find subtracted from three times the number. Find the number.the number.

2(x+3)=3x-92(x+3)=3x-92x+6=3x-92x+6=3x-92x-3x= -9-62x-3x= -9-6-1x= - 15-1x= - 15-1x -1x = = -15-15-1 -1-1 -1X=15 X=15

Ok, you talked me into one more…Ok, you talked me into one more…

The sum of three consecutive numbers is thirty-three. What are The sum of three consecutive numbers is thirty-three. What are the numbers?the numbers?

First: x Second: x+1 Third: x+2First: x Second: x+1 Third: x+2

(x)+(x+1)+(x+2)=33(x)+(x+1)+(x+2)=333x+3=333x+3=333x+3-3=33-33x+3-3=33-33x=303x=303x 3x = = 303033 33X= 10X= 10

Therefore the 3 consecutive numbers are, 10 + 11 + 12 = 33Therefore the 3 consecutive numbers are, 10 + 11 + 12 = 33