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.