1TH/vwo §9.4 Equations

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 1

§ 9.4 Equations

We build on, on the work we already did in § 9.1,  § 9.2 and § 9.3!

Equations are similar to formulas.  Only now with just one variable. 

The dutch word for 'equation'  is: 'vergelijking'. An equation always has an  '=' sign!   For example: 3 x a = 6

This last variable we can now calculate!

Confused? You won't be, if you pay full attention to this Lesson Up!      First we will do a complete exercise together.

§ 9.4 Equations

Examples:

FORMULA:       c + 7 = b                           EQUATION:           c + 7 = 10

The dutch word for 'equation'  is: 'vergelijking'. 

Equations and formulas always have an  '=' sign!  

Confused? You won't be, if you pay full attention to this Lesson Up!      First we will do a complete exercise together.

Look at the difference:

1.   3c = 18.     What value is c ?

2.  78 = 15a + 3.   What value is a ?

Are they equally difficult?

-   Open your Notebook and write down 

          '24'  in the margin (kantlijn).

-   Make 24a in a minutes time

24a The deposit is .....

solution 24a:

Make this task in your Notebook.

6.85 euros you fill in in place of ......
in the formula:
d = 0.25n + 3.60

1. d
2. n
3. 3.60

Solution 24 b:

You fill in 6.85 euros for variable d !

This is because d represents the deposit.

24c What amount did she get for the crate?

Make this one in your Notebook, again.

24c For the crate she gets....
The formula is: d = 0.25n + 3.60

1. 3.85
2. 3.60
3. 6.85

Solution 24c:

3.60 euros she gets for the crate;

it is the fixed amount that you get for the crate,

no matter how many bottles you bring back.

-  Make this in your Notebook.

-  Do you remember that she gets back 6.85 euros in total?

For the empty cola bottles she gets back ...

1. 6.85
2. 3.60
3. 3.25

Solution 24 d:

Jill gets back:

6.85 - 3.60 = 3.25 euros for the empty bottles

(6.85 was the total amount she got back and

3.60 she got for the crate.)

- Make this in your Notebook.

- Do you remember: she got back 3.25 euros for the empty bottles?

And for every bottle she gets 25 cents.   

Jill returned ... cola bottles.

1. 12
2. 11
3. 13
4. 10

Solution 24e:

Jill returned:

3.25 : 0.25 = 13 empty cola bottles.

My compliments for your work up to now!

After my compliment some Theory follows.

When you know the result (or outcome) of a formula 

you have what is called an equation! 

e.g. Formula     a  = 40n + 20

we know a= 140 and we want to calculate what n is equal to.

then the equation is 

                            140 = 40n + 20

In other words working backwards  is:

finding out which value you would have to fill in for the variable to get the result.

(The result or outcome is known already.)

This is called solving the equation

and 

the value for the variable is called the solution to the equation.

Let's study an exercise together.

But first comes up a spring joke!

Final task:  FOTOVRAAG !

a = 4t + 45

If you know that a = 61, then what is the value of t ?

Give your answer in the next slide.

a = 4t + 45
If you know that a = 61, then what is the value of t ?
Give your answer in the next slide.

SOLUTION Final task:

a = 4t + 45

If you know that a = 63, then the equation is:

63 = 4t + 45

4t = 63 - 45 = 18

t = 18 : 4 = 4.5        

Homework:

Havo and H/V:   Support (or Standard) path, skipping 24, 26 and 28 and

                                                                         doing S26 and S28 instead

Vwo:                       Challenge path, so skipping 24, 26 and 28 and

                                                                          doing  C7 and C8 instead

Also Check on your work with the Solutionsbook!