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Buying Protein Bars and Magazines

Alignments to Content Standards: 7.RP.A.3


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?


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.