# Problem of the Week Problem B and Solution Orange You Glad?

## Problem

Betsy is shopping for orange juice. She has discovered that it comes in a variety of containers at different prices.

• At one store, a $$2.63\,$$L container of orange juice costs $$\4.00$$, and a pack of eight $$200\,$$mL orange juice boxes costs $$\2.64$$.

• At another store, $$2\,$$L of orange juice costs $$\3.59$$.

• At both stores, concentrated orange juice in a $$295\,$$mL can costs $$\1.71$$. (This must be mixed with three cans of water to obtain $$4 \times 295 = 1180\,$$mL of drinkable juice.)

Which purchase will give Betsy the best value for her money?

## Solution

The $$2.63$$ L container of orange juice costs $$\4.00\div 2.63 \approx \1.521$$ per litre. Since $$100$$ mL is $$\frac{1}{10}$$ of a litre, the cost is approximately $$\1.521\div 10 = \0.1521$$ or $$15.2$$¢  per $$100$$ mL.

The $$8$$-pack costs $$\2.64$$ for $$1600\,$$mL, or $$\2.64\div 1600=\0.00165$$ per mL.
This is equal to $$\0.00165 \times 100= \0.165$$ or $$16.5$$¢  per $$100$$ mL.

The $$2$$ L container costs $$\3.59\div 2=\1.795$$ per litre. Since $$100$$ mL is $$\frac{1}{10}$$ of a litre, the cost is $$\1.795\div 10=\0.1795$$ or about $$18$$¢  per $$100$$ mL.

The frozen concentrate costs $$\1.71 \div 1180\approx \0.00145$$ per mL.
Therefore, the cost is approximately $$\0.00145 \times 100= \0.145$$ or $$14.5$$¢  per $$100$$ mL.

The cost per $$100$$ mL for each item is summarized in the completed table below.

Amount of Orange Juice Price Price per $$100\,$$mL
$$2.63\,$$L $$\4.00$$ $$15.2$$¢
$$8\times 200=1600\,$$mL $$\2.64$$ $$16.5$$¢
$$2\,$$L $$\3.59$$ $$18$$¢
$$1180\,$$mL (mixed from concentrate) $$\1.71$$ $$14.5$$¢

Since the concentrated orange juice has the lowest price of $$14.5$$¢  per $$100$$ mL, the best value for her money is the concentrated orange juice.