# 3.4 Solving simple problems by forming and solving equations

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## 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.

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.

find the 15th term of the geometric sequince whose first is 18 and last term of 387
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hmm well what is the answer
Abhi
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20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
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
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
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Abhi
is it a question of log
Abhi
🤔.
Abhi
Commplementary angles
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Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
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Kim
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China
Cied
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I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
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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
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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
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