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


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

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


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.