Puzzle

[rosie25]

Please can anybody help me solve this puzzle ?

A movie producer earns 5 million every time he wins an award at a film festival, but loses 2 million every time he fails to win. He has won 70 million after 21 festivals. How many awards has he won ?

Many thanks in advance.

[sandyRoe]

He's won 16. = 80 million and the 5 he lost cost him 10 million subtract the 10 from the 80

[rosie25]

Many thanks

[factor-fiction]

The easiest way is trial and improvement/iteration. Try something you think is close- e.g. won 12 lost 9 and see how close you are (60m less 18m= 42m.) This is too low so try something higher such as won 18 lost 3 (90m-6m=84 m: too high). So go somewhere in between until you get there.

Or you can solve 2 simultaneous equations: 5W- 2F= 70 and W+F= 21.
The second can be rewritten as 2W +2F=42. So 7W= 122, so W = 16

[factor-fiction]

Typo-alert- 7W=112, but W is still 16!

[Arti]

Oops, seems your answer, Sandy, wasn't good enough; thank heavens factor came to the rescue.

[sandyRoe]

He's here because i asked how to do it using a formula. I found the answer because it was relatively easy.

[Arti]

Apologies, FF

[factor-fiction]

Hello Arti. I was also trying to set out a method for rosie so she could see how to do these in future if she wanted.

[Arti]

Again, FF, apologies. I'm not in the best of moods at the mo.

[factor-fiction]

It's okay, Arti. I'm well aware that some of my posts when fired off also don't come out as intended or the intended humour is lost.

[Arti]

Very magnanimous, FF :)