Thread: Ratio problem

Hope someone can help with this problem:

On a sports day of a school, each competitor was given 3 drink coupons while each non-competitor was given 2 drink coupons. The ratio of the numnber of pupils to the number of coupons given was 6:17. What fraction of the pupils in the school competed in the sports day?

Appreciate if you can show detail workings.

Lets say there were x xompetitors and y non competitors
So total noumber of people = x+y

No . coupons for competitors = 3x

No. of coupons for non-competitors = 2y

So total number of coupons = 2y+3x

Hence

$\displaystyle \frac{x+y}{2y+3x} = \frac{6}{17}$

Now go ahead

Spoiler:

$\displaystyle 17x+17y = 12y+18x$

$\displaystyle 5y = x$

But we need to get the fraction of students who participated with total number of students

$\displaystyle \frac{x}{x+y} = \frac{5y}{y+5y}= \frac{5}{6} $