1) Find the amount of increase or decrease. To do that we will use the following equation:

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1 7.4 Percent Increase or ecrease To do the percent increase or decrease problems we will need to break the problem into two parts. 1) Find the amount of increase or decrease. To do that we will use the following equation: The amount of increase or decrease = % of increase or decrease Notice this is similar to the equation we used in Section ) Find the new amount, after the increase or decrease. We will do the following, depending on whether it is an increase or decrease: Percent Increase The new amount the amount of increase Percent ecrease The new amount the amount of decrease Note: Parts 1 and 2 are interchangeable, depending on what the problem asks you. Example 1: A salesperson is granted a 5% salary increase. If the salesperson s current salary is $4,000 per month, what will be his new salary? Solution: We need to find the salesperson s new salary. The percent increase and his current salary are given. To find the salesperson s new salary, we must first find the amount of increase. 1) Find the amount of increase, The amount of increase = % of increase The amount of increase = % of increase I I I 200 The amount of increase is $200. 2) Use the amount of increase from part 1 to find the new amount, The new amount the amount of increase N 4000 N N 4200 So, the salesperson s new salary is $4,200 per month. 200 You Try It 1: A computer technician is granted a 4% salary increase. If the salesperson s current salary is $2,800 per month, what will be his new salary? 1

2 Example 2: A salesperson making a salary of $4,500 per month has his salary increase to $5,000 per month. What is the percent increase? Solution: We need to find the percent increase. His original and new salary are given. Since we are given the original and new salary, we are going to start with part 2 and find the amount of increase. We will then use the amount of increase to do part 1 and find the percent of increase. 2) Use the given original salary and new salary to find the amount of increase, The new amount the amount of increase I I 500 The amount of increase is $500. 1) Use the amount of increase (from above) to find the percent of increase, The amount of increase = % of increase The amount of increase = % of increase I 500 P P P I 0.1 P We got a decimal as our answer so we still need to change the decimal to a percent % So, the percent increase is 11.1%. You Try It 2: A statistician making a salary of $3,200 per month has his salary increased to $3,368 per month. What is the percent increase? 2

3 Example 3: ue to a mill closure, the population of Silvertown decreases by 8.5%. If the original population was 10,200 people, what is the new population? Solution: First, notice this is a decreasing problem. Therefore, we will need to use subtraction. We need to find the new population. The percent decrease and the original population are given. To find the new population, we must first find the amount of decrease 1) Find the amount of decrease, The amount of decrease was 867 people. 2) Use the amount of decrease from part 1 to find the new population, The new population the amount of decrease N N 9333 So, the population is 9,333 people. N 867 You Try It 3: Several retail stores close and the population of Athens decreases by 7.2% as a result. If the original population was 12,500 people, what is the new population? 3

4 Example 4: Millertown falls on hard times and its population decreases from 11,256 people to 10,923 people in the span of one year. What is the percent decrease, rounded to the nearest hundredth of a percent? Solution: We need to find the percent decrease. The original and new population are given. Since we are given the original and new population, we are going to start with part 2 and find the amount of decrease. We will then use the amount of decrease to do part 1 and find the percent of decrease. 2) Use the given original salary and new population to find the amount of decrease, The new population the amount of decrease The amount of decrease is 333 people. 1) Use the amount of decrease (from above) to find the percent of decrease, 333 P P P P We got a decimal as our answer so we still need to change the decimal to a percent % 2.96% So, the percent decrease is 2.96%. You Try It 4: A textile mill closure results in the population of the adjacent town decreasing from 8,956 people to 7,800 people. What is the percent decrease in the population, rounded to the nearest tenth of a percent? 4

5 Note: A discount is a decrease in price. Example 5: A pair of skis is marked at $310. However, the sign in the shop indicates that skis are being discounted at 15%. What will be the new selling price of the skis? Solution: Since a discount is a decrease in price, we will use the decreasing formula. We need to find the new selling price. The percent decrease and the original price are given. To find the new price, we must first find the amount of decrease 1) Find the amount of decrease, The amount of decrease was $ ) Use the amount of decrease from part 1 to find the new price, The new price the amount of decrease 310 N N So, the new selling price of the skis is $ N You Try It 5: A pair of hiking boots is marked at $200. uring a sale, the boots are discounted by 8%. What is the new price of the boots? 5

6 Example 6: A pair of ski boots marked at $210 is sold for $180. Find the percent discount, correct to the nearest tenth of a percent. Solution: We need to find the percent discount or in other words, the percent decrease. The original and new price are given. Since we are given the original and new price, we are going to start with part 2 and find the amount of decrease. We will then use the amount of decrease to do part 1 and find the percent of decrease. 2) Use the given original price and new price to find the amount of decrease, The new price the amount of decrease The amount of decrease is $30. 1) Use the amount of decrease (from above) to find the percent of decrease, 30 P P P P We got a decimal as our answer so we still need to change the decimal to a percent % 14.3% So, the percent discount is 14.3%. You Try It 6: A computer marked at $2,000 is sold at a discount for $1,850. Find the percent discount, correct to the nearest tenth of a percent. 6