Question

http://drlockettjcmaths.weebly.com/uploads/1/8/5/5/18553066/coin_problem.jpg - anyone know how to do this using functions? PLEASE!

Answer 1

Is there a specific function we're to use, or are we supposed to make up one? :)

Answer 2

make up one,but i honestly find it impossible :(

Answer 3

Well, I've been told I'm pretty good at making things up ^.^

Answer 4

then can you help? PLEASEEEEEEEEEEEEEEEEEEEEEEEE<3

Answer 5

Well, you did say please :D

Answer 6

First, why don't we make up a function that tells you how much money Owen has after x-days...?

Answer 7

Let's call it g(x)

Answer 8

alrighty

Answer 9

Well, after x-days, how much money will Owen have left?

Answer 10

thats so confusing. ok so..em... but wait,we dont know whats x

Answer 11

Yeah, we don't know... but we do know how much he'll have left after x-days...

Answer 12

For instance, how much money does Owen start with?

Answer 13

1.10

Answer 14

110 cents :)
After one day, how much is left?

Answer 15

its the same thing :P
105 cents

Answer 16

Yeah, it's the same, but I find it easier if it's just cents.
After two days, how much is left?

Answer 17

100 cents

Answer 18

A dollar :D
Okay, leave it at 100 cents :)
We can keep going like this, or you can observe that after x-days
Owen has
110 - 5x
cents left
Did you notice that? :)

Answer 19

ohhhh i get it! because 5x is 5 times the amount of days which was 2 so thats 10,which leaves it as 100 cents! :D

Answer 20

Yeah. So, answer this quickly... how much does Owen have left after 20 days?

Answer 21

10

Answer 22

See? :)
So, we have a function that tells us how much Owen has left after x-days
g(x) = 110 - 5x [cents]

Can you make a similar function for how much John has left?

Answer 23

emm..... i guess :D so i'll call this one f(x). f(x)= 180-10x ?

Answer 24

Actually, you're very correct :)

Answer 25

yay:') thank you! its easier than it seems:O

Answer 26

But that's not done yet....
We can make a new function
h(x) = g(x) - f(x)

Answer 27

hmmmmm

Answer 28

In other words, the difference between the amount Owen has left and the amount John has left.

Answer 29

What's g(x) - f(x) ?

Answer 30

i..dont know.. hm. (110-5x)-(180-10x)?

Answer 31

Yeah, simplify that :)

Answer 32

emm... 70+5x?

Answer 33

redo that... you made a slight error :)

Answer 34

-70?

Answer 35

in my calculator the answer to : (110-5x)-(180-10x) is 20?

Answer 36

Peter Pan..fell alseep:(

Answer 37

Nonsense....

Answer 38

Next time you suspect that, though, type @PeterPan
I'll be here in a flash :>

Answer 39

what is?

Answer 40

oh ok

Answer 41

Anyway,
(110 - 5x) - (180 - 10x) = 5x - 70

Answer 42

hey that is KIND OF what i said! :P

Answer 43

No... you said 70 + 5x
Which is completely different :P

Answer 44

nope,it has a 70 and a 5x in it so im kind of right ;)

Answer 45

In fact, if we worked with that, our answer would be farther than the second star to the right :D

Answer 46

Also, a wrong answer that's close, is still wrong, and would give you no more points than an outrageously wrong answer :)

Answer 47

alright alright youre right :O but now what,whats 5x in this case?

Answer 48

Relax :)
h(x) = 5x - 70
this is the difference between Owen's and John's money after x-days right?

Answer 49

yup

Answer 50

So, when does Owen have more money? When their difference is positive!
So, at what value of x does 5x - 70 become positive?

Answer 51

my calculator says 20

Answer 52

But what do *you* say?

Answer 53

i dont know :(

Answer 54

Well, when is 5x - 70 = 0?
Go ahead, solve it ^.^
I'll wait...

Answer 55

hmmm..... i learnt about this before, one sec..... 5x-70=0 70-70 would be zero...so i THINK its right to turn the 5x into 70 which would be...14?

Answer 56

YES :D

Answer 57

So after 14 days, they'd have the same amount of money, right? Because the difference is zero, if x =14.

Answer 58

yup :D

Answer 59

So, what happens after 15 days?
How much money would Owen have?
And how much for John?

Answer 60

well hmmm...john should have 30 cent ..

Answer 61

no wait

Answer 62

Yes, John should have 30 cents :)

Answer 63

And Owen?

Answer 64

....20 cent?

Answer 65

No... remember, we had a function for determining how much Owen would have after x-days...

Answer 66

oh yesss! 110-5x=110-5(15)=110-75=35?

Answer 67

Yes, 35 cents :)
See? After 15 days (which is one day after the day they had the same amount)
Owen, with 35 cents, now has more than John, who has 30.

Case Closed ^.^

Answer 68

Awwwwwh thank you so much! I think I'll be the only one in the class who's actually got it all worked out(our class is slightly under average)

Answer 69

No problem :)

Answer 70

Of course, It'll keep until 18 days, when John finally has 0 left
and Owen would have 110 - 5(18) = 110 - 90 = 20 cents left :)
So from day 15 to day 18 (the last day)
Owen would have more

Answer 71

Thank you!

Answer 72

@PeterPan

Answer 73

Yes?

Answer 74

I've got 2 more function questions..:(

Answer 75

We'll see about them :)

Answer 76

Oki dokie,well the second one if a part of the first one:
Q1.a. Let 'h' be the function \[h:x \rightarrow x ^{2}-3x\] .Express h(t) and h(2t+1) in terms of t.
b. Hence,find the values of t for which h(t)=h(2t+1) .
The clue our teacher gave us is that 't' is 'x'

Answer 77

is not if* sorrry

Answer 78

Yeah, your teacher is right :)
Just replace x with t, to get h(t)

Answer 79

but i dont understand the whole express h(2x+1) in terms of x and stuff..

Answer 80

Well, replace all the x's with (2t+1) and see what you get :)

Answer 81

ohhh that makes much more sense

Answer 82

but then why does it say 'express h(x) AND h(2x+1). how do i know whats h(x)?

Answer 83

no, it actually says h(t) and h(2t+1)

Answer 84

but t is x

Answer 85

I'm sure what the teacher meant with that is you replace the x with t

Answer 86

right okay. so still i dont understand how am i meant to find the h(t). in fact i dont understand the whole question >.<

Answer 87

ohhhh i understand it!

Answer 88

That was fast...

Answer 89

so where it says h:x it means h(t) but then..how do i find h(t)?

Answer 90

Like I said... replace all the x's in h(x) with a t.

Answer 91

thats what i did. and so now its like this: \[h:t \rightarrow t ^{2}-3t\]

Answer 92

Yeah, that's it :)
So
h(t) = t^2 - 3t

Answer 93

so then 'express h(t) and h(2t+1)in terms of t. so what do i do with the whole h(2t+1)?

Answer 94

replace x with 2t+1 instead.

Answer 95

so..\[h:t \rightarrow 2^{2 } + 1 ?\]

Answer 96

No...

Answer 97

then..im completely lost

Answer 98

h(x) = x^2 - x
h(t) = t^2 - t
h(2t+1) = (2t+1)^2 + (2t+1)
Simplify.