# 9.1 Use a problem solving strategy  (Page 5/6)

 Page 5 / 6

One number is eight more than twice another. Their sum is negative four. Find the numbers.

−4, 0

One number is three more than three times another. Their sum is negative five. Find the numbers.

−2, −3

Consecutive integers are integers that immediately follow each other. Some examples of consecutive integers are:

$\begin{array}{c}\phantom{\rule{0.2}{0ex}}\\ \phantom{\rule{0.2}{0ex}}\\ \phantom{\rule{0.2}{0ex}}\\ \phantom{\rule{0.2}{0ex}}\\ \hfill \text{...}1,2,3,4\text{,...}\hfill \end{array}$
$\text{...}-10,-9,-8,-7\text{,...}$
$\text{...}150,151,152,153\text{,...}$

Notice that each number is one more than the number preceding it. So if we define the first integer as $n,$ the next consecutive integer is $n+1.$ The one after that is one more than $n+1,$ so it is $n+1+1,$ or $n+2.$

$\begin{array}{cccc}n\hfill & & & \text{1st integer}\hfill \\ n+1\hfill & & & \text{2nd consecutive integer}\hfill \\ n+2\hfill & & & \text{3rd consecutive integer}\hfill \end{array}$

The sum of two consecutive integers is $47.$ Find the numbers.

## Solution

 Step 1. Read the problem. Step 2. Identify what you are looking for. two consecutive integers Step 3. Name. Let n = 1 st integer n + 1 = next consecutive integer Step 4. Translate. Restate as one sentence. Translate into an equation. Step 5. Solve the equation. Combine like terms. Subtract 1 from each side. Divide each side by 2. Substitute to get the second number. Step 6. Check: Step 7. Answer the question. The two consecutive integers are 23 and 24.

The sum of two consecutive integers is $95.$ Find the numbers.

47, 48

The sum of two consecutive integers is $-31.$ Find the numbers.

−15, −16

Find three consecutive integers whose sum is $42.$

## Solution

 Step 1. Read the problem. Step 2. Identify what you are looking for. three consecutive integers Step 3. Name. Let n = 1 st integer n + 1 = 2 nd consecutive integer n + 2 = 3 rd consecutive integer Step 4. Translate. Restate as one sentence. Translate into an equation. Step 5. Solve the equation. Combine like terms. Subtract 3 from each side. Divide each side by 3. Substitute to get the second number. Step 6. Check: Step 7. Answer the question. The three consecutive integers are 13, 14, and 15.

Find three consecutive integers whose sum is $96.$

31, 32, 33

Find three consecutive integers whose sum is $-36.$

−11, −12, −13

## Key concepts

• Problem Solving Strategy
1. Read the word problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don't understand, look them up in a dictionary or on the internet.
2. Identify what you are looking for.
3. Name what you are looking for. Choose a variable to represent that quantity.
4. Translate into an equation. It may be helpful to first restate the problem in one sentence before translating.
5. Solve the equation using good algebra techniques.
6. Check the answer in the problem. Make sure it makes sense.
7. Answer the question with a complete sentence.

## Practice makes perfect

Use a Problem-solving Strategy for Word Problems

In the following exercises, use the problem-solving strategy for word problems to solve. Answer in complete sentences.

Two-thirds of the children in the fourth-grade class are girls. If there are $20$ girls, what is the total number of children in the class?

There are 30 children in the class.

#### Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
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?
s. Reply
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
Devang Reply
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
Abhijith Reply
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?
s. Reply
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 ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
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
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
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.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Mueller Reply
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
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.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
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)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply

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