Maths homework -please help

[THK]

I have reached the answer through trial and error (it has taken me an hour with pennies), & yet I cant explain mathematically how to do this to my 8 year old. Im a rusty maths mum in need of help and hope someone can help give clear idea how to answer this!!

Q: queen esmerelda has 20 gold coins to share between 4 servants
Number 1 has 4 more than number 2
Number 2 has one less than number 3
Number four gets twice as many as number 2
How many do all 4 servants receive.
show workings out.

Thank you :)

Number 2 sounds like the best person to start with. Pretend she has a bagful and draw how many the others have in comparison:

Number 1: bag + 4
Number 2: bag
Number 3: bag + 1
Number 4: bag + bag

Altogether you've got five bags + 5 coins.

So the 5 bags contain 15 coins altogether, giving three in each bag.

It's pre-algebra reasoning - I love algebra!

Such a neat solution and at 7am too.

lostinafrica, I think I love you

You're very kind!

I've been a SAHM so long now, I was thrilled to have some mathematical thinking to start my day! :)

Am a secondary maths teacher in my other life - as if you couldn't tell.

LostinAfrica

Thanks for making it look so simple ...Im definately missing a math gene as I cant understand how you have reached the 15 coins???
There were 20 originally? please help me understand!!I do understand the idea of creating the 5th bag.
Thanks for your early morning patience (confused)

There are 20 altogether - the extra 5 are there split between Number 1 and Number 3.

So the amounts are

Number 1 - 7
Number 2 - 3
Number 3 - 4
Number 4 - 6

I'm confused(I am very easily confused!) and hopeless with maths although I did pass my o'level back in the day! I would have read it as the total coins shared between them has to add up to 20.

1 has 7
2 has 3
3 has 4
4 has 6

but I only could explain getting to this answer by dividing the bags into 5 each and then trial and error also. I'm so looking forward to my dc's maths homework when it gets to this level.

Because you have 20 coins. 5 bags + 5 coins.
20 coins - 5 coins means there must be 15 coins in the 5 bags.
I'm no maths teacher but hope I've explained this well enough

Sorry, that was in answer to THK asking how you knew there were -5 coins in the 5 bags. Got interrupted whilst posting so it took longer and other posts snuck in!

not -5 coins, 15 coins. Obviously

5 bags + 5 coins = 20 coins

so

5 bags = 20 -5 coins

so

5 bags = 15 coins

so

1 bag = 3 coins

Hi wildmutt - Yes I also got there by trial and error.. it bothers me that I just cant understand how to do this:{
Noah - Im still not getting where the extra 1 comes from to make a total of 5 additonal coins as the question says number 2 has 1 less than number 3 ..? please help me understand, Im hoping the penny will drop :o
Thank you.

or let number of coins=x(mystery number)

1 gets x+4
2 gets x
3 gets x+1
4 gets 2x (2 times x )

if you substitute 1 for x the coins are

1=5,2=2,3=4,4=4
5+2+4+4=10 so not enough

but if you substitute 2 for x
you get 10+2+4+4 =20
Bingo!

I don't undersdtand why some people are talking about bags when there is no mention of bags in the problem.

This is problem solving and the strategy is trial and error.

At age 8, you need to use trial and error and work through it systematically, not come up with a highly mathematical explanation.

Maddylou- Yes I tried this way too but it doesnt give the correct answer to the amount each servant receives.
I reached 7,3,4,6, which seems correct but only by playing around with pennies.

You are right, THK. And you need to play around with pennies.

Pointydog - This question was the last one on the worksheet expressing numbers as fractions and vice versa ie changing hours and minutes into fractions.
I was thinking it was about breaking down the 20 coins into parts 4 parts of 20 using the fraction method - but maybe Im making it more difficult than it is??

So it doesn't come under Problem Solving? Or could it?

I really think you are over-thinking it.

Sorry will look again later--7,3,4,6 seems correct

7,3,4,6 is correct

lostinafrica has given a briliant explanation. She has a mystery amount (say one bag of coins). Using the information given you can work out that each servant has the following (as in lostinafrica's original post:

Number 1: bag + 4
Number 2: bag
Number 3: bag + 1
Number 4: bag + bag

Altogether you've got five bags + 5 coins.

You asked where the 15 coins came from - it's because you are told there are 20 coins in total. You know that the 20 coins are equal to five bags + 5 coins so therefore the five bags must have 15 coins in them in total and therefore each bag has 3 coins in.

This is all about problem solving and reasoning.

It's a problem solving question from the standards site, designed for Y3 and 4.
Trial and error, with a systematic approach for the higher ability children is what the teacher is looking for, definitely not fractions.
There's a whole pack of them, so get ready for next week!

HerculesP
YEAY - Finally got it
Thank you :) :) :)

I would do it like this (I don't get the bag thing either). To avoid number confusion, I'd call the servants, say a colour.

No 1 = Red
No 2 = Blue
No 3 = Yellow
No 4 = Green

Red has Blue + 1
Blue has Yellow - 1
(Yellow has Blue + 1)
Green has Blue x 2

Blue is the key.

So, trial and error, what if Blue had 2?

Then:

Red - 6
Blue - 2
Yellow - 3
Green - 4
Total - 15 Not enough, try again

So what if Blue has 3

Red - 7
Blue - 3
Yellow - 4
Green - 6

Total = 20 Bingo!

Goblinchild - oh no !
:(
Please can you refer me to the website so I can start sweating practising.
thks

Yep-see it now

I rushed last bit

If x=3==servant 2

then servant 1 gets 3+4 =7

and servant 3 gets 3+1=4

and servant 4 gets 2x 3 =6

Is that better?