For our question, we do not know the percent. We know that $40 is the original, and that’s $32 is the “after. "
For our example, type 32, hit divide, type 40, hit equals. This division gives us: 0. 8. (It’s not the final answer. )
Because the price in the example dropped, and the price that we calculated is also a discount, we’re on the right path. If the price in the example dropped from $40 to $32, however, and we got 120% after our calculation, we’d know that something is wrong because we’re looking for a discount and we got an increase.
Problem #1: “A $50 blouse is now $28. What was the percentage of discount?” To solve it, grab a calculator. Enter ‘28,’ hit divide, enter ‘50,’ hit equals; the answer is 0. 56. Convert ‘0. 56’ to ‘56%’. Compare this number to 100%, subtracting ‘56’ from ‘100’, leaving us with a discount of 44%. Problem #2: “A $12 baseball cap is $15 after tax. What was the sales tax percentage?” To solve it, grab a calculator. Enter ‘15’, hit divide, enter ‘12’, hit equals; the answer is 1. 25. Convert ‘1. 25’ to ‘125%’. Compare this to 100%, subtracting ‘100’ from ‘125’, leaving us with an increase of 25%.
For example, 67% becomes 0. 67; 125% becomes 1. 25; 108% becomes 1. 08, etc. Divide the percentage by 100, and drop the percent mark. This expresses the percentage as a decimal.
25 x . 40 = ? Remember that we subtracted our sale price of 60% from 100, giving us 40%, and then turned it into a decimal.
25. x . 40 = ? Multiply the two numbers together and we get ‘10’. But ‘10’ what? 10 dollars, so we say that the new jeans cost $10 after the 60% sale.
Problem #1: “A $120 pair of jeans is on sale at 65% off. What is the sale price?” To solve: 100 - 65 gives 35%; 35% converts to 0. 35. 0. 35 x 120 equals 42; the new price is $42 (and quite a deal it is, too!) Problem #2: “A colony of 4,800 bacteria grows by 20%. How many bacteria are there now?” To solve: 100 + 20 gives 120%; that converts to 1. 2. 1. 2 x 4,800 equals 5,760; there are now 5,760 bacteria in the colony.
To solve these questions, you must understand that percentages are applied using multiplication. Whether it is an increase or decrease, it was applied using multiplication. Your job, therefore, is to undo that multiplication. You are not undoing the increase or decrease; you are undoing the application of the percentage. Therefore, three things will be true: You will be dividing by the percent. If you have an increase, you will still add the percentage to 100. If you have a decrease, you will still subtract the percentage from 100.
Let’s imagine we have to work out the following problem: “A video is on sale at 75% off. The sale price is $15. What is the original price?” Sale is another word for discount, so we’re dealing with a decrease. $15 is our “after amount,” because it’s the number we have after the sale has been applied.
Because we’re dealing with a decrease/discount, we’ll subtract 100 - 75, giving us 25%.
25% becomes 0. 25.
Grab a calculator, punch in ‘15,’ hit divide, enter in ‘0. 25,’ and hit equals.
15 divided by 0. 25 = 60, which means the original price was $60. If you want to double-check your answer to make sure it’s correct, multiply the sale price (75%, or 0. 75) with the original price ($60) and see if you get the sale price. ($15): 0. 75 x 60 = $45 sale; $60 (original price) - $45 (sale amount) = $15 (sale price)
This is an increase situation, so add 100 + 22. Convert the answer to a decimal: 122% becomes 1. 22 On a calculator, enter ‘1,525’, hit divide, enter ‘1. 22’, hit equals. Label the answer. For this problem, 1,525 divided by 1. 22 = 1250, so the original investment was $1,250.
