At first a price was decreased by 12%, then it was discounted again by an additional 5%. what is the percent of the total discount? its not 17%

Hello there! So a discount is a takeoff of the original price. We can test out two numbers to see what is the percent of the total discount is.
Say that a pair of shoes costs $50 and there is a 12% discount on them. Even though 12% of that price is taken off, you still have to pay 88% of the total price. 88% is 0.88 in decimal form. 50 * 0.88 is 44.
Now, because the shoes haven't been sold yet, there is a 5% discount on that price. You still have to pay 95% of that price. 44 * 0.95 is 41.8. Now, we can divide that number by the initial price. 41.8/50 is 0.836 or 83.6% in percent form. Let's subtract that by 100% to get the discount. 100 - 83.6 is 16.4. 16.4%.
We can try to see if it works for other numbers. 100 * 0.88 is 88. 88 * 0.95 is 83.6. Percents are parts of 100 and 100 - 83.6 is 16.4. There. The percent of the total discount is 16.4%.

Multiplication property of zero