# Problem of the Week Problem A and Solution Perfect Punch

## Problem

Su is going to make punch for her friends. She wants to mix $$3$$ L of orange juice, $$1$$ L of pop, $$\frac{1}{2}$$ L of grape juice, and $$300$$ mL of cranberry juice in a punch bowl.

1. To avoid spilling, Su plans to use a punch bowl with a capacity of at least $$200$$ mL more than the liquid it holds. What is the smallest capacity that her punch bowl should have?

2. Su has cups that can each hold $$300$$ mL of punch. How many of these cups can she fill with the punch she makes?

## Solution

1. The smallest capacity of the punch bowl is the sum of the volumes of each liquid, plus the $$200$$ mL of extra space to avoid spilling.

One way to calculate this would be to convert all the volumes to millilitres.

• $$3~\text{L} = 3000$$ mL

• $$1~\text{L} = 1000$$ mL

• $$\frac{1}{2}~\text{L} = 500$$ mL

So the minimum capacity is $$3000 + 1000 + 500 + 300 + 200 = 5000$$ mL.

Alternatively, we might notice that the sum of the volume of cranberry juice and the extra room for spillage is: $$300 + 200 = 500$$ mL or $$\frac{1}{2}$$ L.

So the minimum capacity is $$3 + 1 + \frac{1}{2} + \frac{1}{2} = 5$$ L.

2. The volume of punch is $$3000 + 1000 + 500 + 300 = 4800$$ mL.

We can use skip counting to figure out how many cups of punch Su can fill:

$$300$$, $$600$$, $$900$$, $$1200$$, $$1500$$, $$1800$$, $$2100$$, $$2400$$, $$2700$$, $$3000$$, $$3300$$, $$3600$$, $$3900$$, $$4200$$, $$4500$$, $$4800$$

We can see from this that Su can fill $$16$$ cups with punch.

Alternatively, we can calculate the number of cups of punch by dividing $$4800 \div 300 = 16$$ cups.