8.1.20 Going Down, Going Up

This activity involves working out increases and decreases together.

Activity symbolActivity: Going Down, Going Up

Let’s say you live and shop in Maryland, which in 2010 had a 6% sales tax. You have set your eyes on a new dresser for your room, which is on sale at 30% off. Have you ever asked yourself if it makes a difference if the discount is applied first, and then sales tax, or if it is done in the opposite order: Sales tax applied first, and then the discount?

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Comment

Try a numerical example first to get a feel for the problem. For example, what happens if the price of the dresser was $100 (before the discount and sales tax have been applied)?

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Answer

If the item costs $100, reducing the price first gives equation left hand side dollar times 100 minus dollar times 30 equals right hand side dollar times 70.

The sales tax is 6% of $70, which is $4.20.

So, the final bill is dollar 70 postfix plus dollar 4.20 equals dollar 74.20.

Now, let's try it the other way.

Adding the sales tax first gives equation left hand side 1.06 multiplication dollar times 100 equals right hand side dollar times 106.

The discount is 30% of $106, which is equation left hand side 0.3 multiplication dollar times 106 equals right hand side dollar times 31.80.

So, the total bill is dollar 106 postfix minus dollar 31.80 equals dollar 74.20.

It does not seem to matter whether the discount or the sales tax is applied first. But can you be sure? Doing more numerical examples would confirm it. However, these could just be lucky picks. Let’s analyze what we can tell using these particular discount/sales tax rates.

If the discount is 30%, the price after the discount will be 100 percent negative 30 percent equals 70 percent of the original cost. You can find the discounted base price by multiplying the cost by 0.7.

If the discount is applied first, then the sales tax, it’s 106% of 70% of the original price, and can be expressed as 1.06 multiplication 0.7 postfix multiplication original price.

If the sales tax is applied first, then the discount, it’s 70% of 106% of the original price, and can be expressed as 0.7 multiplication 1.06 postfix multiplication original price.

Since it does not matter in which order the multiplication operations are carried out, the answer will be the same using either method. This will work with any type of discount and sales tax.

8.1.19 Online Shopping

8.1.21 Working Backwards