Punch for everyone

This punch needs three parts fruit juice, one part lemon juice and four parts water. For six friends, each gets four hundred millilitres, so you need two thousand four hundred millilitres in all.

Juice $J$, lemon juice $L$ and water $W$ are in the ratio $J:L:W=3:1:4$. For $6$ friends with $400$ ml each: $V=6\times 400=2400$ ml.

$J:L:W=3:1:4$; $n=6$ friends, $V=6\times 400=2400$ ml.

Three and one and four make eight parts, and each part is three hundred millilitres. So take nine hundred of juice, three hundred of lemon juice and twelve hundred of water.

That is $3+1+4=8$ parts, each $\frac{2400}{8}=300$ ml: $(J,L,W)=(900,300,1200)$ ml.

$\frac{2400}{8}=300$ ml a part; $(J,L,W)=(900,300,1200)$.

Stir well, taste, and pour into six equal glasses. Leave it in the cold for an hour.

Stir, taste, pour into $6$ equal glasses and chill for $1$ hour.

Stir, taste; $6$ glasses; chill $60$ min.

If a seventh friend arrives, do not make the glasses smaller; make more punch. Seven times four hundred is two thousand eight hundred, so each part is three hundred and fifty: one thousand and fifty of juice, three hundred and fifty of lemon juice and fourteen hundred of water. The ratio is the same, so the taste is too.

A seventh friend: the glasses do not shrink. $V=7\times 400=2800$ ml, each part $350$ ml: $(J,L,W)=(1050,350,1400)$. The ratio is still $3:1:4$.

$n=7,V=2800$, so $(J,L,W)=(1050,350,1400)$, ratio still $3:1:4$.