Section 6.2: Percent Equations and Percent Increase and Decrease

******When Hiro and his co-workers had lunch at a restaurant near their work, the bill amount was $90.50. They want to leave 18% of the total bill as a tip. How much should the tip be?*******

$16.29 We are looking for the amount of tip that they should leave. Let t be the amount of tip. They want the tip to be 18% of the total bill, $90.50. Translating this into an equation, we have The tip is 18% of the total bill The tip (t) is (=) 18% (0.18) of (*) the total bill (90.50) Multiplying, we have t=16.29 So, they should leave a $16.29 tip.

The bill amount for Dino's lunch was $19.45. He wanted to leave 20% of the total bill as a tip. How much should the tip be?

$3.89

Sales of video games and consoles fell from $1.15 million to $1.03 million in 1 year. Find the percent decrease. Round the answer to the nearest tenth of a percent. For example, if the answer is 34.08% enter 34.1%.

10.4%

*******Hernando's salary was $49,500 last year. This year his salary was cut to $44,050. Find the percent decrease. Round to the nearest percent. For example, if his salary was decreased by 20% you would enter "20".

11% We are asked to find the percent decrease in Hernando's salary. The amount of decrease is given by old amount−new amount=decrease 49,500−44,050=5,450 We can now find the percent decrease by finding what percent the amount of decrease is of the original amount. In other words, we want to find what percent 5,450 is of 49,500.Let p be the percent. The question statement can be translated as follows: 5,450 is what percent of 49,500 To solve for p, we can now divide each side by 49,500 and simplify. 5,450p=49,500p p=0.110 To convert p to a percent, multiply 0.110 by 100. p=0.110 =11%

*******Translate and solve: 537.05 is what percent of 467?

115% Let p be the percent. The question statement can be translated as follows: 537.05 is what percent of 467? 537.05 (537.05) is (=) what percent (p) of (*) 467 (467) 537.05 = p*467 To solve for p, we can now divide each side by 467 and simplify. 537.05=467p p=1.15 To convert p to a percent, multiply 1.15 by 100. p=1.15 =115% It follows that 537.05 is 115% of 467.

Cherise deposits 8% of each paycheck into her retirement account. Her last paycheck was for $1,485. How much did Cherise deposit into her retirement account?

118.8 We are looking for the amount deposited to Cherise's retirement account. Let d be the amount deposited. The amount deposited is 8% of her paycheck, $1,485. Translating this into an equation, we have The amount deposited is 8% of her paycheck d=0.08*1,485 Multiplying, we have d=118.8 So, the amount deposited to Cherise's retirement account was $118.80.

For the first year of his car insurance policy, Tom pays $77 per month. Tom's payments are reduced to $65 per month in the second year as a reward for good driving. What is the percent decrease? Round to the nearest tenth of a percent.

15.6% We are asked to find the percent decrease in Tom's car insurance. The amount of decrease is given by old amount−new amount77−65=decrease=12 We can now find the percent decrease by finding what percent the amount of decrease is of the original amount. In other words, we want to find what percent 12 is of 77.Let p be the percent. Translate the question statement into an equation.1212is=what percentpof⋅7777?To solve for p, we can now divide each side by 77 and simplify.12p=77p=0.156To convert p to a percent, multiply 0.156 by 100.p=0.156=15.6%It follows that the percent decrease in Tom's car insurance was 15.6%.

The tuition at a college increased from $45,000 in 2006 to $52,000 in 2007. What is the percent increase in tuition? Round to the nearest tenth of a percent.

15.6% We are asked to find the percent increase in tuition. The amount of increase is given by new amount−old amount52,000−45,0000=increase=7,000 We can now find the percent increase by finding what percent the amount of increase is of the original amount. In other words, we want to find what percent 7,000 is of 45,000.Let p be the percent. Translate the question statement into an equation. 7,0007,000is=what percentpof⋅45,00045,000? To solve for p, we can now divide each side by 45,000 and simplify. 7,000p=45,000p=0.156 To convert p to a percent, multiply 0.156 by 100. p=0.156=15.6% It follows that the percent increase in tuition was 15.6%.

*******Translate and solve: 3,984 is what percent of 24.9?

16,000 Let p be the percent. The question statement can be translated as follows: 3,984 is what percent of 24.9? 3,984 (3,984) is (=) what percent (p) of (*) 24.9 (24.9) To solve for p, we can now divide each side by 24.9 and simplify. 3,984p=24.9 p=160 To convert p to a percent, multiply 160 by 100. p=160 =16,000% It follows that 3,984 is 16,000% of 24.9.

*******When Hiro and his co-workers had lunch at a restaurant near their work, the bill was $90.50. They want to leave 18% of the total bill as a tip. How much should the tip be?

16.29 We are looking for the amount of tip that they should leave. Let t be the amount of tip. They want the tip to be 18% of the total bill, $90.50. Translating this into an equation, we have the tip is 18% of the total bill t=0.18*90.50 Multiplying, we have t=16.29. So they should leave an $16.29 tip.

****After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21lb. What was Lisa's original weight?

175lb We are looking for Lisa's original weight. We are given that 21lb is 12% of her original weight. Let a be the amount, and translate this into an equation: 21lb is 12% of her original weight. 21lb (21lb) is(=) 12% (0.12) of (*) her org weight (a) 21=0.12a Dividing both sides of the equation by 0.12, we have 21=0.12a a=175 So, Lisa's original weight was 175lb.

****Tim left a $9 tip for a $50 restaurant bill. What percent tip did he leave?*****

18% We are looking for the percent of the tip. We know that Tim left a $9 tip for a $50 restaurant bill. Let p be the percent of the tip, and translate this into an equation: The tip means 9 is means = what percent means p of means * the restaurant bill means 50 Dividing both sides of the equation by 50, we have 9 = 50p p=0.18 So, the percent of the tip was 18%.

The price of a share of one stock fell from $8.75 to $8.54. Find the percent decrease *******DECREASE ******. Round to the nearest tenth of a percent.

2.4% We are asked to find the percent decrease in the price of a share of one stock. The amount of decrease is given by ***old amount−new amount=decrease*** 8.75−8.54=0.21 We can now find the percent decrease by finding what percent the amount of decrease is of the original amount. In other words, we want to find what percent 0.21 is of 8.75.Let p be the percent. The question statement can be translated into an equation. 0.21 is what percent of 8.75? 0.21 (0.21) is (=) what percent (p) of (*) 8.75 (8.75) To solve for p, we can now divide each side by 8.75 and simplify. 0.21=8.75p p=0.024 To convert p to a percent, multiply 0.024 by 100. p=0.024 =2.4% It follows that the percent decrease in the price of a share of one stock was 2.4%.

A grocery store reduced the price of a loaf of bread from $2.80 to $2.73. Find the percent decrease. Round your answer to one decimal place.

2.5% We are asked to find the percent decrease in the price of a loaf of bread. The amount of decrease is given by old amount−new amount=decrease 2.80−2.73=0.07 We can now find the percent decrease by finding what percent the amount of decrease is of the original amount. In other words, we want to find what percent 0.07 is of 2.80. Let p be the percent. The question statement can be translated as follows: 0.07 is what percent of 2.80? 0.7 = p * 2.80 To solve for p, we can now divide each side by 2.80 and simplify. 0.07=2.80p p=0.025 To convert p to a percent, multiply 0.025 by 100. p=0.025 =2.5% It follows that the percent decrease in the price of a loaf of bread was 2.5%.

Angel received a raise in his annual salary, from $55,400 to $56,785. Find the percent increase. Round your answer to the nearest tenth.

2.5% We are asked to find the percent increase in Angel's annual salary. The amount of increase is given by new amount−old amount=increase 56,785−55,400=1,385 We can now find the percent increase by finding what percent the amount of increase is of the original amount. In other words, we want to find what percent 1,385 is of 55,400.Let p be the percent. Translate the question statement into an equation. 1,385 is what percent of 55,400? 1,385 (1,385) is (=) what percent (P) of (*) 55,400 (55,400) To solve for p, we can now divide each side by 55,400 and simplify. 1,385=55,400p p=0.025 To convert p to a percent, multiply 0.025 by 100. p=0.025 =2.5% It follows that the percent increase in Angel's annual salary was 2.5%.

Annual student fees at the University of California rose from about $4,000 in the year 2000 to about $12,000 in 2010. Find the percent increase.

200% We are asked to find the percent increase in student fees. The amount of increase in student fees is given by new amount−old amount=increase 12,000−4,000=8,000 We can now find the percent increase by finding what percent the amount of increase is of the original amount. In other words, we want to find what percent 8,000 is of 4,000.Let p be the percent. The question can be translated into an equation. 8,000 is what percent of 4,000? 8,000 (8,000) is (=) what percent (p) of (*) 4000 (4,000) To solve for p, we can now divide each side by 4,000 and simplify. 8,000=4,000p p=2 To convert p to a percent, multiply 2 by 100. p=2 =200% It follows that the percent increase in student fees was 200%.

A grilled chicken salad at a popular fast food restaurant contains 650mg of sodium, which is 27% of the recommended daily amount. What is the total recommended daily amount of sodium? Round to the nearest milligram.

2407 mg We are looking for the total recommended daily amount of sodium. We are given that 650mg of sodium is 27% of the recommended daily amount. Let a be the amount, and translate this into an equation: 650mg of sodium is 27% of the recommended daily amount 650mg of sodium (650) is (=) 27% (0.27) of (*) the recommended daily amount (a) 650=0.27a Dividing both sides of the equation by 0.27, we have 650=0.27a a≈2,407 So, the recommended daily amount of sodium is about 2,407 milligrams.

****One serving of wheat square cereal has 7 grams of fiber, which is 28% of the recommended daily amount. What is the total recommended daily amount of fiber? Give your answer in grams.

25 grams Step 1. Read the problem. Step 2. Identify what we are looking for. the total amount of fiber that is recommended daily Step 3. Name what we are looking for. Choose a variable to represent it. Let p= total amount of potassium. Step 4. Translate. Write a sentence that gives the information to find it. For fiber, 7 grams is 28% of the total amount. Translate into an equation. 7=0.28⋅p Step 5. Solve the equation. Divide by 0.28. 25=p

Trong has 12% of each paycheck automatically deposited to his savings account. His last paycheck was for $2,165. How much money was deposited to Trong's savings account?

259.80%

The price of a share of one stock rose from $12.50 to $50. Find the percent increase.

300% We are asked to find the percent increase in the price of a share of one stock. The amount of increase in the price of a share of one stock is given by new amount−old amount50−12.50=increase=37.50 We can now find the percent increase by finding what percent the amount of increase is of the original amount. In other words, we want to find what percent 37.50 is of 12.50.Let p be the percent. The question can be translated as follows:37.5037.50is=what percentpof⋅12.5012.50?To solve for p, we can now divide each side by 12.50 and simplify.37.50p=12.50p=3To convert p to a percent, multiply 3 by 100.p=3=300%It follows that the percent increase in student fees was 300%. FEEDBACK

*******One serving of trail mix has 67 grams of carbohydrates, which is 22% of the recommended daily amount. What is the total recommended daily amount of carbohydrates? Round to the nearest gram.

305 grams We are looking for the total recommended daily amount of carbohydrates. We are given that 67 grams of carbohydrates is 22% of the recommended daily amount. Let a be the amount, and translate this into an equation: 67 grams of carbohydrates is 22% of the recommended daily amount. 67 grams of carbohydrates (67) is (=) 22 (0.22) of (*) the recommended daily amount. (a) 67=0.22*a a=305 So, the recommended daily amount of carbohydrates is about 305 grams.

*****Translate and solve: What number is 344% of 107? Round to the nearest hundredth.

368.08 Let n be the number. The question statement can be translated as follows: what number is 344% of 107? n=3.44*107 Now we can find n by multiplying the numbers on the right-hand side. n=3.44⋅107 n=368.08 It follows that 344% of 107 is 368.08.

The nutrition fact sheet at a fast food restaurant says the fish sandwich has 380 calories, and 171 calories are from fat. What percent of the total calories are from fat?

45% We are looking for the percent of the total calories that are from fat. We know that 171 of the 380 calories are from fat, and we want to know what percent this is. Let p be the percent, and translate this into an equation: 171 calories are what percent of the total calories? 171=p*380 171 calories are what percent of the total calories? 171 calories (171) are (=) what percent (p) of(*) the total calories (380) Dividing both sides of the equation by 380, we have 171p=380 p=0.45 So, 45% percent of the total calories are from fat.

In 1995, the standard bus fare in Chicago was $1.50. In 2008, the standard bus fare was $2.25. Give your answer as a percentage value. Find the percent increase of the bus fare in Chicago.

50% Step 1. Read the problem. Step 2. Identify what we are looking for. the percent increase Step 3. Name what we are looking for. Choose a variable to represent it. Let p= the percent. Step 4. Translate. Write a sentence that gives the information to find it. First find the amount of increase. new amount − original amount = increase 2.25−1.50=0.75 Find the percent. Increase is what percent of the original amount? The number 0.75 is what percent of 1.50? Translate into an equation. 0.75=(p)(1.50) Step 5. Solve the equation. 0.75=1.50p Divide by 1.50. 0.5=p Change to percent form; round to the nearest tenth. 50%=p The new fare represents a 50% increase over the old fare.

The population of North Dakota was about 672,000 in 2010. The population is projected to be about 630,000 in 2020. Find the percent decrease of the population of North Dakota. (Round to the nearest tenth of a percent.)

6.3 Step 1. Read the problem. Step 2. Identify what we are looking for. the percent decrease Step 3. Name what we are looking for. Choose a variable to represent that quantity. Let p= the percent decrease. Step 4. Translate. Write a sentence that gives the information to find it. First find the amount of decrease. 672,000−630,000=42,000 Find the percent. Decrease is what percent of the original amount? The number 42,000 is what percent of 672,000? Translate into an equation. 42,000=(p)(672,000) Step 5. Solve the equation. 42,000=672,000p Divide by 672,000. 0.0625=p Change to percent form; round to the nearest tenth. 6.3%=p The population is projected to decrease by 6.3%.

Translate and solve: 286.02 is what percent of 454?

63%

During the financial crisis of 2008, the price of a barrel of Brent crude oil fell from a high of $140 per barrel to around $50 per barrel. What is the percent decrease in the price of oil that occurred during this period? Round to the nearest tenth of a percent.

64.3% We are asked to find the percent decrease in the price of oil. The amount of decrease is given by old amount−new amount=decrease 140−50=90 We can now find the percent decrease by finding what percent the amount of decrease is of the original amount. In other words, we want to find what percent 90 is of 140.Let p be the percent. Translate the question statement into an equation. 90 (90) is (=) what percent (p) of (*) 140? (140) To solve for p, we can now divide each side by 140 and simplify. 90=140p p=0.643 To convert p to a percent, multiply 0.643 by 100. p=0.643 =64.3% It follows that the percent decrease in the price of oil was 64.3%.

An employee receives a pay increase from $35,000 per year to $37,500 per year. Calculate the percent increase. Round to the nearest tenth of a percent.

7.1 We are asked to find the percent increase in the employee's annual salary. The amount of increase is given by new amount−old amount37,500−35,000=increase=2,500 We can now find the percent increase by finding what percent the amount of increase is of the original amount. In other words, we want to find what percent 2,500 is of 35,000.Let p be the percent. Translate the question statement into an equation. 2,5002,500is=what percentpof⋅35,00035,000? To solve for p, we can now divide each side by 35,000 and simplify. 2,500p=35,000p=0.071 To convert p to a percent, multiply 0.071 by 100. p=0.071=7.1% It follows that the percent increase in the employee's annual salary was 7.1%.

The population of a town increased from 20,000 people in 1995 to 34,000 people in 2000. What is the percent increase in population?

70% We are asked to find the percent increase in the town's population. The amount of increase is given by new amount−old amount34,000−20,000=increase=14,000 We can now find the percent increase by finding what percent the amount of increase is of the original amount. In other words, we want to find what percent 14,000 is of 20,000.Let p be the percent. Translate the question statement into an equation.14,00014,000is=what percentpof⋅20,00020,000?To solve for p, we can now divide each side by 20,000 and simplify.14,000p=20,000p=0.7To convert p to a percent, multiply 0.7 by 100.p=0.7=70%It follows that the percent increase in the town's population was 70%.

According to Time magazine, the annual global seafood consumption rose from 22 pounds per person in the 1960s to 38 pounds per person in 2011. Find the percent increase. Round your answer to the nearest tenth of a percent.

72.7% We are asked to find the percent increase in the annual global seafood consumption. The amount of increase is given by new amount−old amount=increase 38−22=16 We can now find the percent increase by finding what percent the amount of increase is of the original amount. In other words, we want to find what percent 16 is of 22.Let p be the percent. The question statement can be translated as follows: 16 is what percent of 22? 16 (16) is (=) what percent (p) of (*) 22 (22) 16=p*22 To solve for p, we can now divide each side by 22 and simplify. 16=22p p=0.727 To convert p to a percent, multiply 0.727 by 100. p=0.727 =72.7 It follows that the percent increase in the annual global seafood consumption was 72.7%.