Download Math 015 Section 6.4 Translating Equations

Math 015
Section 6.4
Translating
Equations
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:
Equation:
five less than a number is thirteen
five less than a number = thirteen
n–5
=
13
n = 18
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
Let: x = the number
3x – 8 =
5x
=
5 times the number
Assigning variables to the things
involved in the problem should
be shown as part of your work.
-8 = 2x
-4 = x
Answer:
The number is -4
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
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.
600,000
is
3/10 of the first year students
Let: x = the number of 1st year students.
600,000 =
3 x 10
10
6,000,000 = 3x
2,000,000 = x
Answer: There are 2,000,000 first-year
students at U.S. Colleges
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
=
$50
+
$28 times the # of rolls
Let: x = # of rolls of wallpaper uses
218
= 50 +
28x
168 = 28x
6 = x
Answer: 6 rolls of wallpaper were used for theroom.
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.
(20 – x)
x
20 ft
5 times the
short piece
=
2 times the
long piece
Let:
x = short piece
20 – x = long piece
+
two
5x = 2(20 – x) + 2
5x = 40 – 2x + 2
5x = -2x + 42
7x = 42
x=6
Answer: Shorter piece = 6 ft
Longer piece = 14 ft
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 #
Let:
=
5 less than 3 times the larger #
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