1. Problem Solving Using Equations

2. Math word problems can, in most instances, be translated in math equations and quickly solved. The language of math is similar to any other language, complete with nouns, verbs, adjectives, phrases, sentences etc…

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

4. Translation Math Math English equivalent + Plus, add, increase, greater than, larger, augment - Subtract, minus, negative, decrease,less than,reduce,diminish x Times, of, multiply ÷ Divided, goes into, a certain number of parts X,a,q,t,p,y,z,n,d,g,m,etc. A number, an age, a quantity, a mass, a volume, a certain amount, etc… 7x Seven times a number, a number times 7 N+6 A number increased by 6, 6 larger than a number T-9 A number decreased by 9, 9 less than a number, a number reduced by 9 4x+_7=8 4 times a number plus 7 equals 8 (x)(x) A number times itself

5. Please Translate Together 3x(3g)(23) A number A number doubled The square of a number A number increased by five The sum of a number and fifteen One-half of a number plus the number Six decreased by a number is the number Five times a number plus eight is eighty-five Three consecutive numbers

6. Answers Three times a number Three times a number times 23 X, y, r, etc… 2xXX+5X=15 ½ x + x 6-x=x 6-x=x5x+8=85 X, x+1, x+2

7. Try some on your own Try some on your own A number is doubled the result is twelve Seven times a number is negative fifty-six A number plus twice a number plus three times a number is seventy-five Six less than triple a number is nine The product of five more than a number and six is thirty We get four when we subtract fifteen from twice a number The product of two consecutive numbers is fifty-six Nine times a number plus the number quadrupled is zero

8. Putting this Together to Solve Word Problems Example: If a number is doubled and the result is increased by 4, the sum is ninety four. Find the number. If a number is doubled and the result is increased by 4, the sum is ninety four. Find the number. 2x+4= 94 2x + 4-4=94-4 2x=90 2x = 90 2 2 X= 45

9. Problem Solving (Continued) The larger of two numbers is seven more than five times the smaller. Their sum is sixty-one. What are the numbers? Larger: 5x+7 Smaller: x 5x+7+x=615x+x=61-76x=54 6x = 54 6 6 X= 9 Therefore the smaller number is 9 and the larger is 52 because 5(9)+7=52 Therefore the smaller number is 9 and the larger is 52 because 5(9)+7=52

10. Still more… If three is added to a number and the sum is multiplied by two, the result is the same as nine subtracted from three times the number. Find the number. 2(x+3)=3x-92x+6=3x-9 2x-3x= -9-6 -1x= - 15 -1 -1 X=15

11. Ok, you talked me into one more… The sum of three consecutive numbers is thirty-three. What are the numbers? First: x Second: x+1 Third: x+2 (x)+(x+1)+(x+2)=333x+3=333x+3-3=33-33x=30 3x = 30 3 3 X= 10 Therefore the 3 consecutive numbers are, 10 + 11 + 12 = 33