# Orange Drink

A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?

## Problem

This is a $750$ ml bottle of concentrated orange squash.

It is enough to make fifteen $250$ ml glasses of diluted orange drink.

How much water is needed to make $10$ litres of this drink?

## Getting Started

How much water is needed to make one *glass* of the drink?

How many glasses of drink are there in a litre? In $10$ litres?

What fraction of the made-up drink is water?

## Student Solutions

You might have had to read this problem over several times before you understood it clearly - it wasn't easy! However, we have received many correct solutions and the majority of you tackled it in the same way. Esther explains how she went about solving the problem very well:

The answer is 8 litres.

First I found out how much juice there is in each cup of drink. The 750mls in the bottle makes 15 cups so each cup contains 750/15=50mls.

This means that each cup contains 250-50=200mls of water.

10 litres=10,000mls. We need to know how many cups this is. As each cup holds 250mls we need 10,000/250=40 cups.

Each cup holds 200mls of water so 40 cups will need 200 times 40=8,000mls or 8 litres of water.

Esther also wrote:

There is another way using fractions.

Excellent reasoning Esther, thank you. Pupils from Queens College Junior School used a similar method to the first way Esther described. Greg, Liam, George and Joe from Moorfield Junior School found a slightly different way:

We then worked out how much water was in one litre of drink. This was 800 ml (200ml times 4).

Finally to find out how much water was in 10 litres we multiplied 800 ml by 10.

Alex from Columbia Independent School, MO, USA worked at the problem in a similar way to Esther's second method:

Since we have only 750 ml of Orange drink, then we have 3000 ml, or 3 litres, of water.

So then each glass contains 200 ml of water which means that 80% of the diluted drink is water, because 200 is 80% of 250.

Then I found out that 4 glasses are equal to 1000 ml then I knew that 200 * 4 = 800. I knew that to prepare 1000 ml of orange drink I need 800 ml of water.

Finally, pupils from Wilby School tackled the problem in a slightly different way again. Here is Georgina's solution:

If you have a 750ml bottle of concentrated orange juice you can make 15 cups of juice. Each cup contains 250ml of juice.

I am trying to make 40 cups of juice, I need to know how much water I need.

If I make 15 cups of juice I need 750ml of juice and 3000ml of water.

If Imake 30 cups of water Ineed 1500ml of juice and 6000ml of water.

I cannot make 40 by adding 15 and 30 together so Ihave to make 10 cups. I only need to find out how much water Ineed to make 10 cups because if Iadd how much water Ihave in 30 cups and how much water Ihave in 10 cups together I will get 40 cups worth of water.

In 10 cups there is 2000ml of water. 6000ml + 2000ml = 8000ml.

Thank you very much to all those who sent solutions - even if there isn't room here to mention you personally.

## Teachers' Resources

**Why do this problem?**

This question tackles proportion in a real context. It also needs systematic thinking to sort out the information and take a step-by-step route to the solution.

### Possible approach

### Key questions

How much juice is there in each glass of drink?

How much water is there in each glass of drink?

How many glasses of drink are there in a litre? In $10$ litres?

### Possible extension

### Possible support