Ratio Problem To find how much chocolates David received Three friends divided a bag of chocolates so that David received a fifth the number of chocolates that Fouad did, and Stina received $80$ percent of the the total number of chocolates. 
What is the ratio of the number of chocolates Stina received to the number that David received ? 
I am getting wrong answer .. Now i am confused. 
 A: $D , F , S  $ be number of chocolotes
$S = 80 $ percent of Total number of chocolates $ = 80*(D + F +S)/ 100 $
$$ S = \frac{4*(D+F+S )}{5} ------>Result 1 $$ 
$$ D = \frac{1}{5 }* F $$ 
so $$ F = 5*D $$
express above F in terms of D , and substitute in Result 1 ,and bring S to LHS 
$$ 5S= 4 * ( 6D + S) $$
$$ 5S = 24D + 4S $$
And have $S = 24* D$ ,,,so $\frac{S}{D} = 24$
ratio of the number of chocolates Stina received to the number that David received = $24 :1$
A: Hint: Let $d,f,s$ be the number each received.  Write the equations you are given $$d=\frac 15f \\s=0.8(d+f+s)$$
These equations scale-if all the numbers of a solution are doubled they stay true, so you might as well take $d=1$ and see what comes out.
A: Hand waving:
S made off with  $80\%$ of the candy, $\frac45$, leaving D and F fighting over the remaining $20\%$ or $\frac15$.  Divide this into $6$ parts, each $\frac{1}{30}$, so D can get $1$ and F can get $5$, as required.  So the $\frac SF$ ratio is $$\frac SF=\frac{\frac45}{\frac{1}{30}}=24$$ 
