Sales tax problems were calculated by hand when I was in elementary school. \u00a0Two cultural changes have occurred since then:<\/p>\n
1) \u00a0The widespread use of calculators, often even during elementary years.<\/p>\n
2) \u00a0The use of cards instead of cash.<\/p>\n
Both changes have diluted people’s consciousness of sales tax – but especially, I think, the second one.<\/p>\n
In any case, sales tax word problems still occur now and then. \u00a0Here’s one that’s a little different from merely calculating the tax and adding it to the sticker price:<\/p>\n
Example: If the total price paid, including tax, is a hundred dollars, what must the sticker price have been?<\/strong><\/p>\n Solution: The first step is to invoke the all-powerful “let statement”:<\/p>\n Let x=price before tax<\/p>\n The tax, assuming 12 percent sales tax, will be 0.12x. Therefore,<\/p>\n Total=price + tax<\/p>\n becomes, more specifically,<\/p>\n 100=x+0.12x<\/p>\n Since x=1x, this simplifies to<\/p>\n 100=1.12x<\/p>\n We now divide both sides by 1.12:<\/p>\n 100\/1.12 = x<\/p>\n leading to<\/p>\n 89.29=x<\/p>\n So, the sticker price must have been $89.29 to give the final price, with tax, of $100.<\/p>\n The “let statement” is what makes this approach straightforward. It gives direction to the solver, and clarity to both solver and marker. When facing word problems, the importance of the “let statement” cannot be overemphasized:)<\/p>\n Hope you had a great Thanksgiving. Cheers!<\/p>\n