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.

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?

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.