Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

## #1 2005-12-17 10:55:28

kcleigh2
Member

Offline

The yearly water bill for a child care centre consists of a standing charge of £18 and a rate of 40p for each unit of water used. i have to draw a graph which could be used to find the cost of water up to a maximum of 250 units. and i have to lable this water board A.

i have to use the graph to answer the following

1)   one year 200 units of water are used.what was the water bill for that year.

2) it is decided that the yearly water bill is to be reduced to a maximum of £80. what is the maximum number of units of water that should be used ?

later in the year, water board B sends some literature for their water costs. they make no standing charge, but instead make a single charge of 60p fpr each unit of water used.

so on that same sheet of graph paper i have to draw a line to show the cost of water from this water board to a mximum of 250 units.
then i have to lable this line water board B

1)at what number of water units do the two lines cross ?

2)how can this number be used to decide which water board to use ?

i have had so many goes at this graph and it is really really anoying me please can someone help me i would be very greatful.

thanks from mandy

i am really really really rubbish at maths lol lol lol lol lol lol lol lol lol lol lol lol

## #2 2005-12-17 12:24:57

dublet
Member

Offline

First to draw the graph, you have to figure you the formula.

It says that the bill is £18 as starting point, and then for every unit, it's 40p more.

So the function is

, where x is the number of units, and f(x) gives you the cost in pennies. The result of this, you can call y, thus y = f(x). Now you know both the x and y axes of your graph.

After that you have to find the range of both axes. you know that for x it is between 0 and a maximum of 250 units. Now you can calculate the range for y, which then goes from f(0) to f(250).

Once you have calculated the results of both of those, you need to lay it out on paper, and you can then put two points on the graph: (0, f(0)) and (250, f(250)) (written as (x, y) coordinate pairs). If you have drawn your graph accurately, you should now easily be able to read the results.

For the second part, you have to make another function: g(x), which calculates the cost for water company B. This is essentially the same as formula f(x), except with different values. First, since there is no starting charge, there's nothing to add, so the function is just
.

Now that you know this, you can also calculate g(0) and g(250), in the same way as for the f(x) function. Then plot the values on the graph, and make a direct line between the two.

I hope this is enough help, any further, and I'll be giving you the solution.

## #3 2005-12-17 12:32:23

John E. Franklin
Star Member

Offline

£ and p.  How do you pronounce these?  Pound? Cent?  I am an ignorant New Englander over the Atlantic.

Imagine for a moment that even an earthworm may possess a love of self and a love of others.

## #4 2005-12-17 12:33:36

dublet
Member

Offline

#### John E. Franklin wrote:

£ and p.  How do you pronounce these?  Pound? Cent?  I am an ignorant New Englander over the Atlantic.

Pound and penny.

## #5 2005-12-17 12:34:24

John E. Franklin
Star Member

Offline

Oh, thanks!

Imagine for a moment that even an earthworm may possess a love of self and a love of others.

## #6 2005-12-18 07:18:39

casey02
Guest

LOL this might sound like a am really really stupid but is there any way that you could make that more simpler lol. I am so bad at maths really i am.

thanks

## #7 2005-12-18 07:53:08

dublet
Member

Offline

Simpler?

Is there anything in specific you don't understand?

http://en.wikipedia.org/wiki/Graph_of_a_function

Last edited by dublet (2005-12-18 07:53:31)

## #8 2005-12-18 10:12:35

kcleigh2
Member

Offline

lol anything specific lol all of it really lol you know when you just cant seem to get you head around something no matter how you look at it. Well this is one of them things lol . i am so rubish at maths it is unbelieveable lol sorry for being a pain.

thanks

i am really really really rubbish at maths lol lol lol lol lol lol lol lol lol lol lol lol

## #9 2005-12-18 11:31:47

John E. Franklin
Star Member

Offline

Make units of water the x-axis, which goes to the right.
Make pennys the y-axis, which goes up.
Now imagine a point at the origin, what would this point mean??
It would mean that it is zero pennies for zero units of water.
But this is not true.  You have to pay 1800 pennies even if you
don't use the water.  So put a point 1800 up from the origin.
Does that make any sense??

Imagine for a moment that even an earthworm may possess a love of self and a love of others.

## #10 2005-12-18 13:48:49

dublet
Member

Offline

#### kcleigh2 wrote:

lol anything specific lol all of it really lol you know when you just cant seem to get you head around something no matter how you look at it. Well this is one of them things lol . i am so rubish at maths it is unbelieveable lol sorry for being a pain.

A graph is a plot of a mathematical function. If you have the function f(x) = x, then calling the function for 0..100 will give back 0..100. This makes for a linear function.
If you have to draw a graph from 0 to 100 values of x, you just make the first and second point (because it's a linear function), which has the begin point of (0, f(0)) = (0, 0) and the end point (100, f(100)) = (100, 100).

Now you know the range of both axes, which has to be from 0 to 100, if you use a centimeter for each 10, you can make it 10 by 10 centimetres big. You then put the begin and end point in the area, and draw a direct line.

If the function is f(x) = 2 and you need to make the graph contain all solutions from 0 to 50, then the begin points are (0, 2) and (50, 2). Again you place the two points, and draw a direct line.

You do know how a function works, don't you?

Do you also know about coordinates?

#### Wikipedia wrote:

In the two-dimensional Cartesian coordinate system, a point P in the xy-plane is represent by a tuple of two components (x,y).

* x is the signed distance from the y-axis to the point P, and
* y is the signed distance from the x-axis to the point P.