Question

Of the 18 coins in my pocket, I had a some pennies, twice as many twenty pence pieces and the rest fifty-pence pieces. If I had 4.64 in total, how many of each type of coin did I have.

Answer 1

There are there unknown variables here, so you're going to need three equations. Do you know any of the equations that the word problem describes?

Answer 2

Let's call the three unknowns "P" for penny, "T" for twenty, and "F" for fifty.

Answer 3

What is the relation between Penny, Twenty and fifty?

Answer 4

So one equation is that there are 18 coins:
1. P + T + F = 18

Answer 5

\( T=2P \) and \( F = 18-3P \)

Answer 6

using Chris notation.

Answer 7

=) So we need just one more.

Answer 8

\( Px+Ty+Fz = 4.64 \)

Answer 9

I don't know your system, so i can't assign values to the x,y and z :(

Answer 10

ah, I was thinking P + 20T + 50F = 4.64 (should have lowercased my variables)

Answer 11

heh my bad, by P/T/F I meant the variable names, so p/t/f

Answer 12

4.64 is \( 4.64\$ \) ?

Answer 13

I got it!

Answer 14

ah good question though

Answer 15

@Chris: If penny is P then twenty pence is 20 P ?

Answer 16

I'm assuming that it's actually .01p + .20t + .50f = 4.64

Answer 17

and 1 penny is 1/100th of a dollar?

Answer 18

correct

Answer 19

well, Australian dollars

Answer 20

1 pence = 1 dollar/100

Answer 21

lol, I think they should give this information with the question itself.

Answer 22

Its a british textbook, so I guess we are dealing with £££

Answer 23

this question is easy if you know this information, and if you don't it's impossible to solve with certainty.

Answer 24

haha, so pence = 1 pound/100 right?

Answer 25

I think we have it right ffm

Answer 26

Yes I think that too chris.

Answer 27

three equations:
1. p + t + f = 18
2. p + .2t + .5f = 4.64
3. t = 2p

Where p = number of pennies, t = number of twenty pence, and f = number of fifty pence

Answer 28

Now with this three equation, you could just use substitution and get your desired result

Answer 29

You know how to do that chrissy?

Answer 30

i remember, finding unknown variables using 3 equations

Answer 31

yeah

Answer 32

You guys have me very helpful

Answer 33

*been

Answer 34

since we alreeady have the value of T=2p, substitute to the 2 equation then 2 equations will remain, you can already solve system of 2 equation using elimination and substitution, choose. .

Answer 35

No problem! I think the trickiest part of this problem was that line - "twice as many twenty pence", if you skip over that then you can never get the third equation. t = 2p.

Answer 36

@jerwyn gayo: There are different ways that we could use to solve a system of three equations with three unknowns for example you could use Matrix algebra, but for this purpose the best way is to use substitution.

Answer 37

@ffm. yeah,.