Solving Word Problems With Equations Of One Degree And One Unknown Worksheet With Answers

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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.
2
1
- x
=
42
3
3
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
Twice the sum of two quantities amounts to 42.
4.
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
1

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