Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

SOLVING WORD PROBLEMS

Word problems can be classified into different categories
...
All problems in each category are solved the same way
...

Age Problems
These types of problems ask you to figure out the age of different people by giving you different clues
...
Jim is 4 years less than twice David’s age
...


David’s age = x
Jim’s age = 2 x − 4
John’s age = (2 x − 4 ) + 3
Jim’s age
x + 2 x − 4 + (2 x − 4 ) + 3 = 35
5 x = 40

← Ages of the three boys together equal 35
...

Example:

A cashier has 3 more dimes than nickels and twice as many nickels as quarters
...
05
...


0
...
05(2 x ) + 0
...
05
0
...
10 x + 0
...
30 = 3
...
55 x = 2
...


Distance Problems
Example:

You are driving along at 55 mph when you are passed by a car doing 85 mph
...

Using the rate equation in the form distance = speed • time, or D= s ⋅ t for each car, we
can write:
D = 55 t

and

D + 1 = 85 t

Substituting the first equation into the second 
and solving for t 

55t + 1 =
85t

−30t =
−1
t = 1 / 30 hours or 2 minutes

Geometry Problems
Example:

If the perimeter of a rectangle is 18 inches, and one side is one inch longer than the other,
how long are the sides?
Let one side be x (width) and the other side be x + 1 (length)
...


x

Investment Problems
Example:

Suppose $10,000 is invested at 9% interest
...
12 x + 0
...
11(x + 10,000 )
after multiplying both sides by ‘10’
...
How much of the mix should be used with 1 1/2 gallons of water?
Let x = # of cups of the drink mix to use
14 x
There are 6 quarts in
=
2 6
1 ½ gallons
1
6   = 2x
4
3
= 2x
2
3
x = cup of the drink mix
4

Number Problems
Example:

Find a number such that 5 more than one-half the number is three times the number
...


→

10 + x =
6x
10 = 5 x
x=2

Percent of Problems
Example:

The price of gasoline increased by 25% between January and March
...
15, what was the price per gallon in January?
To find the price in March:
Let:

Price in January + 25% increase in cost = Price in March

price per gallon in January = x
25% increase in cost = 0
...
15

Then x + 0
...
15
1
...
15
x = $0
...
If both employees work together, how long will it take to
assemble 26 radios?
The two together will build 7 + 5 = 12 radios in an hour, so their combined rate is 12 radios
per hour
...


List of Steps to Follow When Solving Word Problems
1
...
Read it
as many times as necessary to understand it
...
Read the problem again and write down details
...
Determine what question is being asked
...
Key words – to determine what unknown quantity you are asked to find, look for key
words such as how many, how much, what is, find, how long
...
Associated words – find the word or words associated with the key words
...

How long will it take for John to save $200?
Determine the percentage increase in the price per unit
...
For complicated problems, it may help to write down in your own words what question
is being asked
...
Write down essential details
...
Make diagrams, charts, or drawings to help you visualize the problem
...
Assign a letter to represent the unknown quantity (or one of the unknowns if there is
more than one) and write down the letter and what it represents
...
Determine what units the solution should have and write this down
...
If there is more than one unknown quantity to find, establish and write down the
relationships among the unknowns
...

Remember that to find a unique solution you must be able to write down as many
equations as you have letters representing unknowns
...
If there are several known quantities given in the problem, it may be helpful to write
them down in tabular form
...
If still unclear as to what is being asked, or can’t find the relationships among the data given, read the
problem again
...
Other
problems may require several readings before the relationships become clear
...

Do not get discouraged
...

4
...

5
...
Identify the unknowns in the problem using the solution you
obtained
...
Check your results
...
One number is 6 less than 3 times another number and their sum is 62
...

2
...
The total number of points scored was 127
...
What is the velocity of a car (in miles per hour) if it goes 40 miles in 35 minutes?
4
...
00 a pound, hazelnuts for $2
...
75 a pound
...
30 a pound so that the profit or loss is unchanged?
5
...
How many cubic centimeters (cc) of each should be
mixed to obtain 150 cc of a solution that is 6% acid?
6
...

Daily overhead is $600
...
Jim is 3 times as old as his cousin and the difference in their ages is 18
...
Maria has scores of 96, 86, and 78 on three tests
...
What are the dimensions of a rectangle whose length is 4 more than twice the width and whose
perimeter is 3 less than 7 times the width?
10
...
If
the smallest board he has is 1 foot in length, what was the length of the original board?
11
...
50 in a week
...
5 hrs
...
What is the hourly rate
for each?
12
...
Their total interest on the two investments was $860
...
Eduardo invested his at 7% and Sofia invested hers at
6%
...
Jennifer got a job as an engineer at a starting salary of $28,000
...
Jennifer will receive an annual increase of $600 and Miguel’s annual
increase will be $1100
...
David can paint the living room in 4 hours and Anna can paint it in 6 hours
...
A restaurant uses 2 pints of milk with 3 pints of cream to make coffee creamier
...
Let x = one numbers
y = another number
x = 3y − 6
x+ y =
62
y + 3y − 6 =
62
4 y = 68
y = 17
3y − 6 =
45 The two numbers are 17 and 45

2
...


40 x
=
35 60
35 x = 2400

x = 68
...
Let x = # of lbs of cashews
# of lbs of hazelnuts = 50 − x
3 x + 2
...
75 ( 50 ) =
2
...
5 x + 87
...
5 x = 17
...
Let x = amount of 10% solution

7

Amount of 4% solution = 150 − x
0
...
04 (150 − x ) =
0
...
Let x = # of items
0
...
85 x

50 x + 60000 =
85 x
x = 1715
7
...
Let x = average score on the next two tests
96 + 86 + 78 + 2 x
≥ 90
5
260 + 2 x ≥ 450

x ≥ 95

9
...
Let x = length of original board
1 x
  =1
43
x = 12 feet

11
...
5 y 109
...
5 y =
150

=
70 x + 95 y
1095
−70 x − 87
...
5 y = 45
y = $6
...
5 ( 6 ) =
109
...
50 Janet's rate is $7
...
00 per hour
9

12
...
08
=
x + 0
...
07 x + 0
...
Let x = # of years until salaries are equal
28000 + 600 x = 24000 + 1100 x
−500 x =
−4000
x = 8 years until their salaries are equal

14
...
4 hours

15

---