# Buying Protein Bars and Magazines

## Task

Tom wants to buy some protein bars and magazines for a trip. He has decided to buy three times as many protein bars as magazines. Each protein bar costs \$0.70 and each magazine costs \$2.50. The sales tax rate on both types of items is 6½%. How many of each item can he buy if he has \$20.00 to spend?

## Solutions

Solution: Using a ratio table

The table below shows the cost for the protein bars and magazines in a 3 : 1 ratio.

Number of magazines | 1 | 2 | 3 | 4 |

Number of protein bars | 3 | 6 | 9 | 12 |

Value of the magazines | \$2.50 | \$5.00 | \$7.50 | \$10.00 |

Value of the protein bars | \$2.10 | \$4.20 | \$6.30 | \$8.40 |

Value of both magazines and candy bars |
\$4.60 | \$9.20 | \$13.80 | \$17.40 |

Cost with tax | \$4.90 | \$9.80 | \$14.70 | \$19.60 |

Looking at the last column of the table, we can see that Tom can buy 4 magazines and 12 protein bars for \$20 and that he cannot afford 5 magazines and 15 protein bars.

Solution: 1 magazine and 3 protein bars as a single unit

Tom’s decision to buy three times as many protein bars as magazines can be thought of as deciding to buy in a unit consisting of 1 magazine AND 3 protein bars.

The cost of a unit then is \$2.50 + 3$\times$(\$0.70), which is \$4.60.

With sales tax, this would be \$4.60 $\times$ 1.065, which when rounded to the nearest cent would be \$4.90, or just under \$5.00.

There are four groups of five in 20 and 4 $\times$ 4.899 = 19.596. This leaves \$0.40 in change. So, with \$20, he can buy 4 magazines and 12 protein bars, with \$0.40 in change.

## Buying Protein Bars and Magazines

Tom wants to buy some protein bars and magazines for a trip. He has decided to buy three times as many protein bars as magazines. Each protein bar costs \$0.70 and each magazine costs \$2.50. The sales tax rate on both types of items is 6½%. How many of each item can he buy if he has \$20.00 to spend?