<< Chapter < Page Chapter >> Page >

Mathematics

Grade 9

Number patterns, graphs, equations,

Statistics and probability

Module 16

Solving simple problems by forming and solving equations

ACTIVITY 1

To solve simple problems by forming and solving equations

[LO 2.2, 2.4]

How do we solve this problem?

Jamie’s dad is four times as old as Jamie. His father is 40. How old is Jamie?

a) We could think really hard, and try a few guesses. For instance: If Jamie is 1 year old, then his father must be 4. Not correct. What about 2 years old? And so on.

b) Make a table: Complete the empty spaces. Does this help?

Age 1 2 3 4
Age x 4 4 8 12 28 40

c) Draw a flow diagram: Is this useful?

  • As you can see, there is not much difference between the three methods – you can use any one that suits you. But they are not really very useful, because you have to do a lot of guessing. If the problems become very difficult, these methods become impossible to use.
  • So we will use a better way.
  • The way to do this problem is to make an equation from the information, and then to solve the equation and use the solution to write down an answer.
  • Making equations is not very easy to start with, but it gets a lot easier with practice.
  • An equation needs an equal sign as well as a variable (we usually use x , but it can be any letter).

Jamie’s dad is four times as old as Jamie. If his father is 40, how old is Jamie?

  • This is the general form of the equation:
  • Four times Jamie’s age = father’s age, which is 40.
  • The question asks Jamie’s age; so we let Jamie’s age be x .
  • Now the equation becomes: 4 x = 40
  • and this asks us to find a number which gives 40 when multiplied by 4. If we divide 40 by 4, we get 10. So x must be 10, and therefore Jamie is ten years old. It is easy to see that this answer is correct.

A problem for you to do: Leon has 48 marbles. Amy has only a third as many as Leon; how many does she have? Use the last method.

The way you should set out your answer is:

State what the variable represents.

  • Write an equation using the variable.
  • Solve the equation.
  • Write down the solution, namely what the value of the variable is.
  • Write down the answer to the problem in words.

Please note that the first and last steps are in ordinary words, and the middle step(s) in algebra.

E x ercise:

Find the answers to the following problems:

1. Mr Jacobs has R295,45 in his pocket. Mrs Jacobs has R55,30 less than her husband in her purse. How much money does she have in her purse?

2. I think of a number. I multiply it by 7 and divide the answer by three. I get 49. What was the number I first thought of? Remember to check your answer.

3. In America Joanie buys an item that is marked $5,75. She works out that it would be R41,69 when she converts the dollars to rand. What is the rand/dollar exchange rate she used?

ACTIVITY 2

To develop effective methods for solving more complicated equations

[LO 2.3, 2.4]

  • We will be doing more word problems, but we have to concentrate more on the algebra in our solutions. Make sure that you know e x actly what each of the steps means and why it is done.
  • Some of the following problems are followed by the solutions. But try to find the answer without looking ahead. Then compare your answer and the way you set it out with the answer.

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
how do you translate this in Algebraic Expressions
linda Reply
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
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
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
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
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele 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
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Mathematics grade 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11056/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Mathematics grade 9' conversation and receive update notifications?

Ask