Express the following as a single discount rate.

25% and 16%

30%, 20%, and 5%

60%, 10%, and 5%

40%, 20%, 121⁄2%, and 4%

25%, 20%, and 3%

331⁄3%, 25%, and 5%

37%

46.8%

65.8%

59.68%

41.8%

52.5%

Step-by-step explanation:

Discount Rates

It's a way to express that a quantity will be reduced to some other by a fixed percentage. For example, taking 40% off a $50 price means:

* Operating 40*50/100=$20 This is the discount

* Subtracting from the original price: $50 - $20 = $30. This is the reduced quantity.

The trick is doing all of that procedure more efficiently to solve the question. At the end of the procedure we did this

50 - 40*50/100 = 50 * (1 - 40/100) = 50 * (1-0.4) = 50 * 0.6 = $30

This means we get the same result by only multipying by a factor which is one minus the discount percentage divided by 100.

Let's start with the first homework

Discount 25% and 16%. The first discount is made by multiplying by 0.75 and the second my multiplying by 0.84. This means that the total discounted value is

0.75*0.84 = 0.63. That is a single discount of 1-0.63 = 37%

Discount 30%, 20%, and 5%. The product is

0.70 * 0.80 * 0.95 = 0.532, a single discount of 1-0.532 = 46.8%

Discount 60%, 10%, and 5%

0.40 * 0.90 * 0.95 = 0.342, a single discount of 65.8%

Discount 40%, 20%, 12 1/2%, and 4%. Let's recall that 12 1/2% = 12.5%. The product is

0.60 * 0.80 * 0.875 * 0.96 = 0.4032. A single discount or 1-0.4032 = 59.68%

Discount 25%, 20%, and 3%

0.75 * 0.80 * 0.97 = 0.582. Single discount of 41.8%

Discount 331/3%, 25%, and 5%

0.66 * 0.75 * 0.95 = 0.475, single discount of 52.5%