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?
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.
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.