Maths question.....

[girt_giggler]

ok, we are sitting in work talking random stuff. a chap has just mentioned a maths question that his daughter got the previous evening for homework. been many a year since ive been at school so can anyone else help figure it out

Susan, John & Elizabeth are playing a dart game.

Susan scores 147 more than John, & 3 times the score of Elizabeth. Combined their scores come to a total  336. What is each individual players scores?

[Croí na hÉireann]

60
207
69

Put it back nifan, I caught a 147 and a 105 anyway... 

[nifan]

aye, need to relearn how to use me calculator:)

[full back]

  nifan
Just missed quoting you

[nifan]

i relaised the flaw in my argument straight away - hoped noone had seen it:)

[girt_giggler]

excellent. how u figure that one out or whats the formula? want to look smart in front of my work colleagues!

[girt_giggler]

still a little double dutch to me!!

[nifan]

to expand it

(147+x) + x + y = 336

and (147+x) =3y    == x = 3y - 147

therefore

147 + (3y - 147) + (3y - 147) + y = 336
7y = 336+147
y=69

and therefore
x = 3*69 - 147
x=60

[David McKeown]

I did it as follows

Let susan score = x
Let john score = y

y = x-147 (1)

Elizabeth score = x/3

Therefore

x + y + x/3 =336

Multiply all sided by 3

3x + 3 y +x =1008

Collect like terms

4x + 3y = 1008

Using (1) above

4x + 3 (x - 147) = 1008

Multiply out bracket

4x + 3x -441 = 1008

Collect like terms

7x = 1449

x = 207

Susan score = 207

John = 207 - 147 = 60

Elizabeth = 207/3 = 69

[David McKeown]

having thought about this, I have just realized where I saw this question before. It was on my Key Stage 3 exam in 1999 back when Pluto was still a planet.