Julian owns a fruit stall selling fruit juice. The tables below give information related to Julian's stall.

1. Calculate the total volume of ice used in one cup.

Volume of one ice cube
$=2\times 2\times 1.5=6\text{ cm}^3$

Volume of 6 ice cubes
$=6\times 6=36\text{ cm}^3$

1. Find the volume of apple juice in one cup after allowing for the ice.

From part (a), volume of ice in one cup $=36\text{ cm}^3=36\text{ ml}$.

Volume of apple juice
$=300-36=264\text{ ml}$

2. Use direct proportion to estimate the sugar content in $264\text{ ml}$ of apple juice.

For apple juice, $75\text{ ml}$ contains $19\text{ g}$ of sugar.

Sugar in $264\text{ ml}$
$=\frac{264}{75}\times 19$
$=66.88\text{ g}$
$\approx 67\text{ g}$

1. Find the volume of mixed fruit juice in the cup and the equal volume from each fruit.

From part (a), volume of ice in one cup $=36\text{ cm}^3=36\text{ ml}$.

Volume of juice in one cup
$=300-36=264\text{ ml}.$

Since equal amounts of juice are used from each of the 3 fruits,
$\frac{264}{3}=88\text{ ml}$
of juice is used from each fruit.

2. Identify the compulsory fruit and choose the lowest-sugar possible recipe for a fair health test.

The fruit with the highest sugar content per fruit is watermelon, since it has $280\text{ g}$ of sugar per fruit.

To minimise sugar content while satisfying the recipe condition, choose the two fruits with the lowest sugar per ml:

$\text{Pineapple: }\frac{89}{630}\text{ g/ml}$
$\text{Watermelon: }\frac{280}{1890}\text{ g/ml}$
$\text{Orange: }\frac{14}{75}\text{ g/ml}$

So consider watermelon, pineapple and orange.

3. Calculate the sugar content contributed by each of the 3 fruits using direct proportion.

Sugar from $88\text{ ml}$ of watermelon juice:
$88\times \frac{280}{1890}=13.04\text{ g}$

Sugar from $88\text{ ml}$ of pineapple juice:
$88\times \frac{89}{630}=12.43\text{ g}$

Sugar from $88\text{ ml}$ of orange juice:
$88\times \frac{14}{75}=16.43\text{ g}$

4. Find the total sugar content in one cup and convert it to teaspoons.

Total sugar in one cup
$=13.04+12.43+16.43=41.90\text{ g}.$

Since $1$ teaspoon of sugar $=5\text{ g}$,
$\frac{41.90}{5}=8.38$
teaspoons of sugar.

5. Make and justify the health decision using the daily recommendation and the context of other sugar sources.

The recommended daily sugar intake is less than
$10\times 5=50\text{ g}.$

One cup of the least sugary possible mixed fruit juice already contains about
$41.9\text{ g}=8.38\text{ teaspoons}.$

This leaves only
$50-41.9=8.1\text{ g}$
of sugar, or about
$10-8.38=1.62$
teaspoons, for all other food products in the day.

Since a typical Singaporean consumes sugar from multiple sources in a day, this drink is too close to the daily limit.