Transcript Solving Verbal Equations

Solving Verbal
Equations
Warm-up

Translate the following into mathematical
expressions

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One number multiplied by the sum of two different
numbers
The product of three different numbers decreased by
a fourth number
A number subtracted from the product of two different
numbers
The difference between two numbers multplied by a
third number.
Warm-up Continued
 Translate
the following into mathematical
expressions




The sum of a number and seven divided by a
different number
The product of fourteen and a number,
decreased by another number
Seven less than a number is nineteen.
A number increased by twelve is the same as
ten added to twice that number.
Verbal Equations
What operation does the phrase tell me to do?

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Product of
Is the same as
Quotient
Decreased by
More than
is

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

Increased by
Divided by
Added to
Less
The quantity of
The difference
How to solve Verbal Equations
 Step
1: Write the algebraic expression
 Step
2: Solve for the variable
 Step
3: Check your answer
Example 1
 Fifteen
is added to two times a number
and the result is fifty-five.
Write the
algebraic
equation
Solve
for the
variable
2n 15  55
2n  40
n  20
Check your
answer.
2  20   15  55
40  15  55
55  55
Example 2
 Two
consecutive integers sum up to 303.
Find the integers.
n   n  1  303
2n  1  303
2n  302
n  151 Am I done?
What do I use to
represent consecutive
integers again?
Example 3
 If
three times a number is decreased by
thirty, the result is equal to two times the
number. Find the number.
3n  30  2n
n  30  0
n  30 Am I done?
Example 4

The last math test that you took had 100 regular
points and 10 bonus points. You received a total
score of 87, which included 9 bonus points. What
would your score have been without any bonus
points?
First
Step
2:
Step:
Fill
Write
in what
your
ayour Regular
Bonus
Total
Step 4:
3: Check
Solve
for
points
points
score
model
you
answer
know
in
words
variable
indicating what you
have.
p  9  87
Are you done?
p  78
Example 5
 The
perimeter of a rectangular shaped lot
is 420 meters. The length is twice the
width. Find both dimensions.

Step 1: draw a picture
2x
x
2x + x + 2x + x = 420
x = 70
Am I
done?
width = 70, length = 140
Example 6

Four people are sharing the cost of a monthly
phone bill of $58.25, what is each person’s
share of the bill?
4 x  $58.25
x  $14.56
Does this cover the
whole bill?
Example 7
The balance in your bank account
is $642.35. If you use your check
card to buy some Halloween
decorations, your balance would be
$476.79. How much do the
decorations cost?
Consecutive Integers
 How
do you represent consecutive
integers? Let’s try representing three
consecutive integers
x
 Why
x+1
x+2
do I add by 1 each time?
Consecutive Even Integers
 How
do you represent consecutive even
integers? Let’s try three of them again.
2x
 Why
2x+2
2x+4
do I multiply the first by 2?
 Why do I add by 2 each time?
Consecutive Odd Integers
 How
do you represent consecutive odd
integers? Hey let’s try three yet again.
2x+1
 Why
2x+3
2x+5
did I multiply by 2 and add 1 the first
time
 Why do I add by 2 each time?
Example 8
 Find
two consecutive integers that sum up
to fifty-three.
x  x 1  53
2x  1  53
2 x  52
26  26  1  53
53  53
x  26
The two integers are 26 and 27
Example 9
 Find
three consecutive integers such that
the sum of the first and third integer is 82.
X + (X + 2) = 82
2X + 2 = 82
2X = 80
X = 40
40, 41, 42
Example 10
 Find
three consecutive even integers
whose sum is 426.
2x  2x  2  2x  4  426
6x  6  426
2(70)  2(70)  2  2(70)  4  426
6 x  420
140  140  2  140  4  426
426  429
x  70
The three integers are 140, 142, and 144
Example 11
 George
is five cm taller than John. The
sum of the heights is 405 cm. How tall is
George?
Then you can write
Let George
What
are webe
looking
our
variable,
for? x
Then define
John in terms of
George.
John = x-5
x   x  5  405
2 x  5  405
2 x  410 205  205  5  405
410  5  405
x  205 405  405
your equation and
solve
George is 205 cm.
Example 12
 The
Lions played twenty seven basketball
games. They won twice as many as they
lost. How many did they win?
Let the number
they lost be x
Number they
won =2x
x  2 x  27
3x  27
x9
The Lions won 18 games.
Example 13
 Find
three consecutive odd integers
whose sum is 33
9, 11, 13