# 9.1 Use a problem solving strategy  (Page 3/6)

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Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was $3$ more than the number of notebooks. He bought $5$ textbooks. How many notebooks did he buy?

2

Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is seven more than the number of crossword puzzles. He completed $14$ Sudoku puzzles. How many crossword puzzles did he complete?

7

In Solve Sales Tax, Commission, and Discount Applications , we learned how to translate and solve basic percent equations and used them to solve sales tax and commission applications. In the next example, we will apply our Problem Solving Strategy to more applications of percent.

Nga's car insurance premium increased by $\text{60},$ which was $\text{8%}$ of the original cost. What was the original cost of the premium?

## Solution

 Step 1. Read the problem. Remember, if there are words you don't understand, look them up. Step 2. Identify what you are looking for. the original cost of the premium Step 3. Name. Choose a variable to represent the original cost of premium. Let $c=\text{the original cost}$ Step 4. Translate. Restate as one sentence. Translate into an equation. Step 5. Solve the equation. Divide both sides by 0.08. Simplify. $c=750$ Step 6. Check: Is our answer reasonable? Yes, a $750 premium on auto insurance is reasonable. Now let's check our algebra. Is 8% of 750 equal to 60? Step 7. Answer the question. The original cost of Nga's premium was$750.

Pilar's rent increased by $\text{4%}.$ The increase was $\text{38}.$ What was the original amount of Pilar's rent?

$950 Steve saves $\text{12%}$ of his paycheck each month. If he saved $\text{504}$ last month, how much was his paycheck?$4,200

## Solve number problems

Now we will translate and solve number problems . In number problems, you are given some clues about one or more numbers, and you use these clues to build an equation. Number problems don't usually arise on an everyday basis, but they provide a good introduction to practicing the Problem Solving Strategy . Remember to look for clue words such as difference , of , and and .

The difference of a number and six is $13.$ Find the number.

## Solution

 Step 1. Read the problem. Do you understand all the words? Step 2. Identify what you are looking for. the number Step 3. Name. Choose a variable to represent the number. Let $n=\text{the number}$ Step 4. Translate. Restate as one sentence. Translate into an equation. Step 5. Solve the equation. Add 6 to both sides. Simplify. Step 6. Check: The difference of 19 and 6 is 13. It checks. Step 7. Answer the question. The number is 19.

The difference of a number and eight is $17.$ Find the number.

25

The difference of a number and eleven is $-7.$ Find the number.

4

The sum of twice a number and seven is $15.$ Find the number.

## Solution

 Step 1. Read the problem. Step 2. Identify what you are looking for. the number Step 3. Name. Choose a variable to represent the number. Let $n=\text{the number}$ Step 4. Translate. Restate the problem as one sentence. Translate into an equation. Step 5. Solve the equation. Subtract 7 from each side and simplify. Divide each side by 2 and simplify. Step 6. Check: is the sum of twice 4 and 7 equal to 15? Step 7. Answer the question. The number is 4.

how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?