Any Mathematicians About?

[sandyRoe]

What's the formula to solve this?

http://www.theanswerbank.co.uk/Quizzes-and-Puzzles/Question1320645.html

[bibblebub]

There are 2 variables: the number of wins (w is an appropriate algebraic letter) and the number of loses (l). So the info given results in 2 equations:-

winnings: 5w - 2l = 70
festivals: w + l = 21

When you add the 2 equations you want to eliminate one of the unknowns so, in this case, double the second equation and add to be rid of l:-

5w - 2l + 2(w+l) = 70 + 2*21

=> 7w = 112
=> w = 16

Then substitute that in one of the equations to get the other variable (2nd equation is simplest):-

l = 21 - w = 5

Thus the solution is: wins = 16, losses = 5

Is that what you want or a more general solution?

[sandyRoe]

Thanks, Bibblebub. I managed to work it out because it was relatively simple. The formula would help however difficult it was

[factor-fiction]

I've just posted something similar on rosie's thread
http://www.theanswerbank.co.uk/Quizzes-and-Puzzles/Question1320645.html
But Bibblebub has given the full calculation whereas I just gave a general indication

[sandyRoe]

Ta to you too, F-F.

[bibblebub]

a₁X + b₁Y = N₁
a₂X + b₂Y = N₂

to be rid of Y multiply 1st equation by b₂, the 2nd by b₁ and subtract one from the other:-

a₁b₂X + b₁b₂Y = N₁b₂
a₂b₁X + b₂b₁Y = N₂b₁

(a₁b₂ - a₂b₁)X = N₁b₂ - N₁b₁

=> X = (N₁b₂ - N₂b₁)/ (a₁b₂ - a₂b₁)

And substitute that back in the equations to get

Y = (N₂a₁ - N₁a₂)/ (a₁b₂ - a₂b₁)


(i think i've got all the subscripts correct)