# 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.

#### Questions & Answers

Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
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
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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?
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Jeannette has $5 and$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
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?