Math 015 Section 6.4 Translating Equations

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Math 015 Section 6.4 Translating Equations
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Translating Sentences into Equations
An equation states that two mathematical
expressions are equal
To translate a sentence into an equation requires
recognition of the words or phrases that mean
equals
equals is is equal to
amounts to represents

Once the sentence is translated into an equation,
the equation can be solved by rewriting into a
form using variables and constants.
Example
Sentence five less than a number is thirteen
Equation

thirteen
five less than a number
n 5

13
n 18
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Assigning variable expressions
Problem Eight less than three times a number
equals five times the number. Find the
number.
8 less than 3 times a number

5 times the number
Let x the number
Assigning variables to the things involved in the
problem should be shown as part of your work.
3x 8
5x

-8 2x
-4 x
Answer The number is -4
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Problem Translate four more than five times a
number is six less than three times the
number into an equation and then solve the
equation.
4 more than 5 times a number

6 less than 3 times the number
Let x the number
5x 4
3x 6

5x 3x 10
2x -10
x -5
Answer The number is -5
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Problem Six hundred thousand of the first-year
students at U.S. colleges are taking at
least one remedial class in reading,
writing, or mathematics. This is three-tenths of
the total number of first-year students.
How many first year students are in U.S.
colleges.
is
600,000
3/10 of the first year students
Let x the number of 1st year students.
10
3 10

x
600,000
6,000,000 3x
2,000,000 x
Answer There are 2,000,000 first-year
students at U.S. Colleges
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Problem A wallpaper hanger charges 50 plus
28 per roll of wallpaper used in a
room. If the total charge for hanging
wallpaper in a room is 218, how many rolls of
wallpaper were used in that room?

Price
28 times the of rolls

50
Let x of rolls of wallpaper uses
218

50

28x
168 28x
6 x
Answer 6 rolls of wallpaper were used for
theroom.
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Problem A board that is 20 ft long is cut
into two pieces. Five times the length of
the shorter piece is 2 ft more than twice the
length of the longer piece. Find the
length of each piece.
x
(20 x)
20 ft
Let x short piece
20 x long piece
5 times the short piece
2 times the long piece

two

5x

2(20 x)
2
5x 40 2x 2
Answer Shorter piece 6 ft
Longer piece 14 ft
5x -2x 42
7x 42
x 6
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Problem The sum of two numbers is 9. Eight
times the smaller numbers is five less
than three times the larger number. Find
the two numbers.

8 times the small
5 less than 3 times the larger
Let x the smaller number
9 x the larger number
8x

3(9 x) 5
8x 27 3x 5
8x -3x 22
11x 22
x 2
Answer The smaller number is 2 The larger
number is 7