184 - The fractions involved in diluting squash with water

I know that in Australia, Hong Kong and the UK, squash is a very popular beverage.

Better known as cordial in the land down under, squash is a fruit-flavored concentrate that has to be mixed with water in order to be made appropriate for drinking. Typically, on the side of the bottle of squash, there are instructions for use, saying it requires the dilution of one part squash to four or five parts water.

I bought some squash about a week ago, and now it's finished. This particular brand of concentrate requires diluting one part squash with nine parts water.

I'm sitting there with my glass, using my fingers as measures, trying to divide the glass into ten equal parts, so that I can solve this mathematical predicament, but it turns out that this arithmetic cannot be done with the mere use of my phalanges as the glass is only nine fingers tall.

So I gather a ruler, a calculator, a piece of paper and a pen, and I try to work out the right amount of cordial needed to achieve the right amounts of concentrate and water. I even factor in the fact that the sides of the glass aren't parallel to each other, the fact that the volume of the glass itself can't be included, and the fact that I'm not going to fill the glass to the brim.

And after fifteen minutes of fiddling with h, r, s, x, y, a, and V, all the while, bringing back painful memories of having to learn integration in calculus class, I simply give up, pour into the glass what I feel is right, get it wrong (of course), and suffer from the horrible blend of superfluous sweetness and overbearing acidity of the drink.

Do the manufacturers expect us to reach into our back pockets and get out our handy-dandy measuring cylinders?

They don't even say 'approximately one part squash to nine parts water' or 'around one-fifth of squash with four-fifths of water'. It's exactly the fractions stated, which makes me feel like I'm wasting the stuff if I don't get it precisely right.

I think I need help.