Math 015 Section 8.2 Percent Equations

Obj: To solve equations involving percents Most percent problems that we will be working with can be written in the form: amount = percent · base This statement can be changed into the proportion amount percent = base 100

Remember what the following words mean in percent equations Obj: To solve equations involving percents Remember what the following words mean in percent equations what of is What is written as an unknown of indicates multiplication is is written as an equal sign

Obj: To solve equations involving percents Example: What is 4% of $85,000 · x = 4% 85,000 4 100 x 85,000 = 100 x = 340,000 x = 3400 4% of $85,000 is $3400

Obj: To solve equations involving percents Example: What is 8.7% of 160 8.7 x = 100 160 100 x = 1392 x = 13.92 8.7% of 160 is 13.92

Obj: To solve equations involving percents 14 Example: Find 15 % of 400 14 x 15 = 400 100 100 x = 6100 x = 61 14 15 % of 400 is 61

Obj: To solve equations involving percents Example: What is 16 % of 66 23 23 16 x = 66 100 100 x = 1100 x = 11 16 % of 66 is 11 23

Obj: To solve application problems A quality control inspector found that 1.2 % of 2500 telephones inspected were defective. How many telephones inspected were not defective. Strategy: 1. find the number of defective phones 2. subtract that number from 2500 Defective phones: What is 1.2% of 2500 x 1.2 = 2500 100 100 x = 3000 x = 30 Answer: 2470 phones were not defective

Obj: To solve application problems A worker’s hourly wage was $23.50 before an 8% raise. What is the new hourly wage? Strategy: 1. find 8% of $23.50 2. add that amount to the original wage What is 8% of $23.50 x 8 23.50 100 = 100x = 188 New wage 23.50 + 1.88 = $25.38 x = 1.88

Obj: To solve equations involving percents Example: 24 is what percent of 60 · 24 = x % 60 24 x 60 100 = 60 x = 2400 x = 40 24 is 40% of 60

Obj: To solve equations involving percents Example: What percent of 40 is 30 ? x% · 40 = 30 x 30 100 40 = 40 x = 3000 x = 75 30 is 75% of 40

Obj: To solve application problems The monthly payment for the Kaminski family is $787.50. What percent of the Kaminski’s monthly income of $3750 is the house payment ? Strategy: What percent of $3750 is $787.50 ? x% · 3750 = 787.50 x 787.50 100 3750 = 3750 x = 78,750 x = 21 Answer: House payment is 21% of the income

Obj: To solve application problems On one Monday night, 31.39 million of the approximately 40.76 million households watching television were not watching David Letterman. What percent of the households were watching Letterman? Round to the nearest percent. 40.76 – 31.39 = 9.37 million were watching What percent of 40.76 is 9.37 ? x% · 40.76 = 9.37 x 9.37 100 40.76 = 40.76 x = 937 x » 22.988 Answer: About 23% of the households were watching

Obj: To solve equations involving percents Example: 18% of what is 900 · x 18% = 900 18 900 100 x = 18 x = 90,000 x = 5000 18% of 5000 is 900

Obj: To solve equations involving percents 15 is 2.5 % of what ? 15 = 2.5% x · 15 2.5 = x 100 2.5 x = 1500 x = 600 15 is 2.5% of 600

Obj: To solve application problems A used car has a value of $10,458 which is 42% of the car’s original value. What was the car’s original value ? Strategy: 10,458 is 42% of what ? 10,458 = 42% · x 10,458 42 = x 100 42 x = 1,045,800 x = 24,900 Answer: The original value is $24,900

Obj: To solve application problems A store has a tennis racket on sale for $89.60 which is 80% of the original price. What is the dollar difference between the original price and the sale price ? Strategy: 1. 89.60 is 80% of what 89.60 = 80% · x 2. subtract $89.60 from that answer 89.60 80 x 100 = 80 x = 8960 x = $112 Original price Answer: The difference is $22.40