A GUIDE TO SOLVING WORD PROBLEMS
1) Read the problem carefully as many times as necessary until you understand the situation.
2) Draw a sketch or diagram, underline any key words, identify any formulas that need to be used.
3) Choose a letter to represent the quantity you want to find and label accordingly.
4) Write an equation and solve.
5) Check the solution with the information in the original word problem. Did you answer the question the problem is asking?
TRANSLATIONWORD PROBLEMS
Word problems that are referred to as translation problems relies on you knowing the key words for your operations.
EXAMPLES:
1) The sum of twice a number and seven is twenty five. Find the number.
Let x = the number.
equation: 2x + 7 = 25
solve: 2x = 18
x = 9
solution: 9 is the number.
2) Fourteen times a number, decreased by the number, is forty-two. Find the number.
Let x = the number
equation: 14x - x = 42
solve: 13x = 42
x = 4
solution: 4 is the number.
3) The sum of half a number, three times the number, and three-fifths the number is equal to the number minus five. Find the number.
Let x = the number
equation:1x + 3x + 3x = x - 5
2 5
solve: 10(1x + 3x + 3x = x - 5)
2 5
5x + 30x +6x = 10x - 50
41x = 10x - 50
31x = -50
x = -50/31
solution:-50/31 is the number.
NOTE: The number refers to a real number. Therefore, the solution can certainly be a fraction, decimal, integer or irrational.
4) Six times the difference of twice a number and tone is equal to the quotient of the number and two. Find the number.
Let x = the number
equation: 6(2x - 1) =x
2
12x - 6 = x/2
2(12x - 6 =x)
2
24x - 12 = x
-12 = -23x
12/23 = x
solution: 12/23 is the number.
5) In an election, Gray received 12344 more votes than Arnold. If 38458 votes were counted, how many votes did each candidate receive?
LetArnold's number of votes = x
Gray's number of votes = 12344 + x
38458 votes is the total number of votes and so Gray's votes plus Arnold's votes must total to that.
equation: (12344 + x) + x = 38458
solve: 12344 + 2x = 38458
2x = 26114
x = 13057
solution:Arnold received 13057 votes
Gray received 25401(12344 + 13057) votes.
NOTE: Solving the equation does not result in answering the question posed in the word problem. Therefore, you must go back and reread the question.
6) Barry is twice as old as Mary. Four years ago, their ages totaled 46. How old are they now?
Since the problem is referring to now and ago, a table will be set up.
Now Four years ago
Barry 2x 2x - 4
Mary x x - 4
equation: totaled indicates that Barry's and Mary's ages are being added.
(2x - 4) + (x - 4) = 46
solve: 3x - 8 = 46
3x = 54
x = 18
solution: Mary is 18 years old and Barry is 36 years old.
The question is asking for their ages now. Therefore, use the"now" labels in your table.
7) The sum of three consecutive integers is 255. Find the integers.
An example of consecutive integers is 4, 5, 6, 7. The pattern is you need to add one to the previous number to get the next one.
Let first integer = x
second integer = x + 1
third integer = x + 2
equation: x + (x + 1) + (x + 2) = 255
solve: 3x + 3 = 255
3x = 252
x = 84
solution: The integers are 84, 85 and 86.
8) The sum of three consecutive even integers is 186. Find the integers.
An example of consecutive even integers is 4, 6, 8, 10. The pattern is you need to add two to the previous number to get the next even number.
Let first integer = x
second integer = x + 2
third integer = x + 4
equation: x + (x + 2) + (x + 4) = 186
solve: 3x + 6 = 186
3x = 180
x = 60
solution: The integers are 60, 62, and 64.
NOTE: If you had gotten an odd number when you solved the equation, then you know that you made a mistake because the question states even integers. This is why you should always check your answers to make sure they fit the problem.
9) The sum of three consecutive odd integers is 381. Find the integers.
An example of consecutive odd integers is 3, 5, 7, 9. The pattern is you need to add two to the previous number to get the next odd number.
Let first integer = x
second integer = x + 2
third integer = x + 4
equation: x + (x + 2) + (x + 4) = 381
solve: 3x + 6 = 381
3x = 375
x = 125
solution: The integers are 125, 127 and 129.
NOTE: The "set up" for the examples 8 and 9 are the same because to get to the next even or odd number you always have to add two.
10) The product of two numbers is 12. One number is five more than than twice the number. Find the numbers.
Let 1st number = x
2nd number = 2x +5
equation: x(2x + 5) = 12solve by factoring
solve: 2x2 +5x = 12
2x2 +5x - 12 = 0
(2x - 3)(x + 4) = 0
x = 3/2 or x = -4
if x = 3/2 then the other number is 2(3/2) + 5 = 8.
if x = -4, then the other number is 2(-4) + 5 = -3.
The numbers are 3/2 and 8 or -4 and -3.