Applied Mathematics

Victoria had 3 dimes, 4 pennies, and 5 quarters. What is the total value of her coins?

$1.59

If Arya's initial investment became $13,000 after 10 years of investing it at a bank that applies a simple annual interest of 3%, what was her initial investment?

$10,000

If Victor invested $700 at a simple annual interest rate of 10%, how much money would he have in 5 years?

$1050

Michelle's investment decreased by one-third in the first year and then doubled in the second year. If her initial investment was $1,800, what was her investment after the second year?

$2,400

How much money was invested at a 4% annual simple interest rate for 2 years to become $2,700?

$2,500

The price of a stock was initially $320. After a 20% increase and then a 30% decrease in stock price, approximately, what is the final stock price?

$269

How much money was initially invested at a 3% interest compounded annually for 2 years to become $1,000?

1,000/1.03^2 (8. Simple and Compound Interest done!)

If Connie invests $1,200 at a bank where investments are compounded bi-annually at a 2% interest rate, how much money would she have in 10 years?

1,200(1.01)^20

How many yards are in 54 inches?

1.5

If Austin is driving one mile per minute, approximately, how many kilometers per second is he driving? (1 mile = 1.6 km)

1.6/60

If $500 is invested at a simple annual interest rate of 10%, how long will it take, in years, for the investment to double?

10

Erin is 5 years older than Kelly. Erin's age is also double that of Kelly's. What is Erin's age?

10 (3. Age problems done!)

Justin's donut shop sold two times as many chocolate donuts as strawberry donuts. His shop also sold three times as many honey-glazed donuts as chocolate donuts. If he sold 600 honey-glazed donuts, how many strawberry donuts did he sell?

100

Connie invests $1,000 at a 10% interest rate. If the investment is compounded annually, how much money would she have in 5 years?

1000(1.10)^5

Ben is 20 years older than Andy. Eight years ago, the sum of their ages was 88. What is the current sum of their ages?

104

Two trains started from the same location. At 7:00 AM, the first train traveled north at a speed of 80 mph. At 8:00 AM, the second train traveled south at a rate of 100 mph. At what time were they 620 miles apart?

11:00 AM

4 gallons of 70% acid solution were mixed with x gallons of 90% acid solution to produce an 85% acid solution. What is the value of x?

12

If compound X has a melting point of 50°C, at what Fahrenheit temperature do you expect Compound X to melt?

122

Andrew has red, green, and blue marbles. He has 3 times as many red marbles as green marbles, and three more blue marbles than green marbles. If he has 2 green marbles, how many marbles does he have in total?

13

When open, a hose fills a water tank in 5 hours. A siphon drains the same water tank in 8 hours. If the water tank is initially empty, how long will it take to fill the tank, to the nearest hour, if both the hose and siphon are opened?

13 hours

How many additional gallons of water is needed to dilute 10 gallons of 50% acid solution to a 20% acid solution?

15 gallons (7. Mixtures-Solutions Problems done!)

If a hose can fill a bathtub in 30 minutes, how long will it take for two hoses working at the same rate to fill the same bathtub?

15 minutes

99 is what percent of 66?

150%

Maurice has (x - 2) dimes and (x + 4) nickels and their total value is (x2 - 100) cents. How many dimes does he have?

18

John can build a bicycle in 3 hours. Dave can build the same bicycle in 6 hours. If they work together, how long will it take them to build the bicycle?

2 hours

Driving at an average speed of 50 miles per hour, Kevin takes 3 hours to get to work. If he drives at 60 miles per hour instead, how long will it take him to get to work?

2 hours 30 minutes

Farook can make 40 sandwiches in 2 hours, while Zain can make 48 sandwiches in 3 hours. Working together, how long would it take them to make 90 sandwiches for a party?

2 hours 30 minutes

If Connie weighs 2240 oz., what is her weight in kg? (1 kg. = 2.2 lbs.)

2240/16 x 2.2

Gemma drives at a constant speed of 70 mph for two hours. Approximately, how many kilometers has she driven? (1 mile = 1.6 km)

225

Ben is 10 years older than Annie. In 16 years, the sum of their ages will be equal to 90. How old is Annie right now?

24

Noah's boat has a crew of captains, navigators, and sailors. There are 6 times as many sailors as captains and one-third as many navigators as sailors. If there are 36 crew members on Noah's boat, how many sailors are there?

24

A car traveling at 100 mph uses 5 gallons of fuel per hour. How many gallons of fuel are needed if the car travels a distance of 500 miles at 100 mph?

25 gallons

If 5 liters of 40% alcohol solution are mixed with 15 liters of 20% alcohol solution, what is the concentration of alcohol in the final mixture?

25%

Jim has two children, Cecelia, and Philip. Cecelia is four years older than Philip, and their ages added together and squared is equal to 100. How old is Philip right now?

3

Lily has 5 more dimes than nickels, 2 more nickels than quarters, and the total value of her coins is $2.00. How many quarters does she have?

3

Sophie has a total of 12 green and blue marbles. She has three times as many green marbles as blue marbles. How many blue marbles does she have?

3

Caroline's GPA increased by 0.6 and then decreased by 0.3. If her final GPA was 3.5, what was her initial GPA?

3.2

Jim blends two types of nuts: almonds ($12 a pound) and cashews ($20 a pound) to produce a new mixture that weighs 40 pounds. If this new mixture costs $14 a pound, how many pounds of almonds will Jim have to add?

30

Leonard is three times as old as Jeff. In 10 years Leonard will only be twice as old as Jeff. How old is Leonard now?

30

Paul needs 50 ounces of 20% salt solution. If he has a 35% salt solution and a 10% salt solution, how many ounces of the 10% salt solution will he need?

30

Sam takes twice as long as Hannah to fix a car. When they work together, they can fix a car in 10 hours. How long does it take Sam alone to fix a car?

30 hours

A doctor has 600 mL of 20% alcohol solution and an unknown amount of 50% alcohol solution. When both solutions are combined, they form a 30% alcohol solution. What is the volume, in milliliters, of the 50% alcohol solution?

300

A chemist combined 8 liters of 40% acid solution and 12 liters of 25% acid solution. What is the concentration of acid for the resulting solution?

31%

Mike drove 20 miles at an average speed of 40 miles per hour. He then drove another 60 miles at an average speed of 30 miles per hour. What was his average speed, in miles per hour, for the entire trip?

32

Pierce's age is double the age of Shirley. Four years from now, the sum of their ages will be 104. How old is Shirley right now?

32

It takes 20 minutes for Kyle to wash a car, and 30 minutes for Yves to wash the same car. If they work together, how long will it take for them to wash three cars?

36 minutes (5. Work-Rate problems done!)

In an international multimedia group, 60% of profits come from social media, and 40% of profits come from television. If international audiences make up 30% of social media profits and 50% of television profits, what percent of all profits came from international audiences?

38%

Robin has 4 more nickels than quarters, and the total value of her coins is $1.40. How many quarters does she have?

4

Jocelyn rows upstream at a speed of 8 mph for 4 hours. She then turns around and rows downstream for 2 hours, until she reaches her starting point. Assuming she rows at a constant pace, what is the speed of the water?

4 mph (6. Distance-Speed problems done!)

How many ounces are in 3 pounds?

48

Joe can make 120 pencils per hour and Kevin can make 500 pencils per hour. If they work together, how long will it take them to make 3100 pencils?

5 hours

What is the annual simple interest rate required for a $1,500 investment to become $1,725 after 3 years?

5%

Convert 3 kilometers per hour into meters per minute.

50 (9. Conversion problems done!)

If x = 7, what percent of (5x + 7) is (4x - 7)?

50%

On a 20% battery, Jamie can drive 100 kilometers in his electric truck. How far can he drive on a full battery?

500 km

Clara Inc. has 4 times as many software engineers as hardware engineers and 3 times as many business analysts as hardware engineers. If there are 72 software engineers, how many business analysts are there?

54

In a class of 80 students, 30% failed the math aptitude test. How many students passed?

56

40% of all employees at a company work in hardware, while 60% of all employees work in software. If 70% of the employees in hardware work from home, and 50% of the employees in software work from home, what percent of all employees work from home?

58%

If the average car loses 20% of its value in the first year, and then 15% of its current value each year after the first year, approximately, what percent of the car's value is left over after 3 years?

58% (2. percentages done!)

A man saw a bear charging towards him. He ran to his car 108 feet away at 9 feet per second, and the bear arrived at the car 6 seconds after him. Assuming the man and bear both traveled the same distance, in feet per seconds, how fast was the bear running?

6

If x divided by three is equal to two times y, what is the value of x divided by y?

6 (1. Translating Words Into Expressions done!)

Jim initially travels 300 miles in 5 hours. If he reduces his speed by 10 miles per hour, how long would it take him to cover the same distance?

6 hours

Roy has 6 quarters, 8 dimes, and x nickels, and their total value is $2.65. Solve for the value of x.

7 (4. Coing problems done!)

Ted has 5 more quarters than dimes, and the total value of his coins is $2.30. How many quarters does he have?

8

If a person sleeps 8 hours per day, how many seconds per week do they spend sleeping?

8 x 7 x 60 x 60

In order to boost exam scores, a professor decided to take the square root of each student's exam score and then multiplied this result by 10 to get the boosted score. If Jack scored 64 on his exam, what was his boosted score?

80

In order to boost exam scores, a professor decided to take the square root of each student's exam score and then multiplied this result by 10 to get the boosted score. If Henry's boosted score is 90, what was his original score?

81

Running at a constant rate, 6 identical machines can produce 180 bags in one hour. At this rate, how many bags could 15 machines produce in 2 hours?

900

How long does it take for Cole to paint the barn alone? 1) Dylan and Cole, who work at the exact same rate, can paint the barn together in 8 hours. 2) Dylan can paint the barn alone in 10 hours. A. Statement 1) alone is sufficient but statement 2) alone is NOT sufficient to answer the question. B. Statement 2) alone is sufficient but statement 1) alone is NOT sufficient to answer the question. C. Both statements 1) and 2) together are sufficient to answer the question but neither statement is sufficient alone. D. Each statement alone is sufficient to answer the question. E. Statements 1) and 2) together are not sufficient to answer the question.

A.

Ron is 12 years older than April, who is 8 years younger than Leslie. What is the sum of their ages? 1) Ron is four years older than Leslie. 2) 16 years ago, Ron's age was double that of April's. A. Statement 1) alone is sufficient but statement 2) alone is NOT sufficient to answer the question. B. Statement 2) alone is sufficient but statement 1) alone is NOT sufficient to answer the question. C. Both statements 1) and 2) together are sufficient to answer the question but neither statement is sufficient alone. D. Each statement alone is sufficient to answer the question. E. Statements 1) and 2) together are not sufficient to answer the question.

B.

Stella has nickels, dimes, and quarters. She has double the number of nickels compared to dimes, and double the number of dimes compared to quarters. How much money does she have? 1) Stella has four times as many nickels compared to quarters. 2) The value of Stella's nickels and dimes combined is $0.80 . A. Statement 1) alone is sufficient but statement 2) alone is NOT sufficient to answer the question. B. Statement 2) alone is sufficient but statement 1) alone is NOT sufficient to answer the question. C. Both statements 1) and 2) together are sufficient to answer the question but neither statement is sufficient alone. D. Each statement alone is sufficient to answer the question. E. Statements 1) and 2) together are not sufficient to answer the question.

B.

A 200-gram bag of nuts consists of peanuts, cashews, and almonds. How many grams of cashews are there? 1) 30% of the nuts by weight are peanuts 2) 35% of the nuts by weight are almonds A. Statement 1) alone is sufficient but statement 2) alone is NOT sufficient to answer the question. B. Statement 2) alone is sufficient but statement 1) alone is NOT sufficient to answer the question. C. Both statements 1) and 2) together are sufficient to answer the question but neither statement is sufficient alone. D. Each statement alone is sufficient to answer the question. E. Statements 1) and 2) together are not sufficient to answer the question.

C.

If Abed's age is double Britta's age, and Britta's age is double Craig's age, which of the following statements cannot be true? A. Abed is four times older than Craig B. Craig is the youngest of the three C. Britta is the oldest of the three D. Britta is younger than Abed

C.

If Adam invested $600 at a bank where interest is compounded, how much will he profit in 5 years? 1) The compound interest rate is 7%. 2) The interest is compounded quarterly. A. Statement 1) alone is sufficient but statement 2) alone is NOT sufficient to answer the question. B. Statement 2) alone is sufficient but statement 1) alone is NOT sufficient to answer the question. C. Both statements 1) and 2) together are sufficient to answer the question but neither statement is sufficient alone. D. Each statement alone is sufficient to answer the question. E. Statements 1) and 2) together are not sufficient to answer the question.

C.

If Toby is older than Kevin, and Kevin is younger than Andy, which of the following statements below must be true? A. Andy is older than Toby B. Toby is older than Andy C. Kevin is younger than both Andy and Toby D. Toby is older than Andy and Kevin

C.

If Train A and Train B are moving toward one another, how long does it take them to pass by each other? 1) The distance between Train A and Train B is 360 miles. 2) Train A is traveling at 45 mph and Train B is traveling at 60 mph. A. Statement 1) alone is sufficient but statement 2) alone is NOT sufficient to answer the question. B. Statement 2) alone is sufficient but statement 1) alone is NOT sufficient to answer the question. C. Both statements 1) and 2) together are sufficient to answer the question but neither statement is sufficient alone. D. Each statement alone is sufficient to answer the question. E. Statements 1) and 2) together are not sufficient to answer the question.

C.

Hannah mixes together two kinds of coffee beans: Arabica, which costs $10 a pound, and Robusta, which costs $15 a pound, to produce a mixture that costs $12 a pound. How many pounds of Arabica coffee beans go into the mixture? 1) The mixture contains 30 pounds of Robusta coffee beans. 2) The total mixture weighs 75 pounds. A. Statement 1) alone is sufficient but statement 2) alone is NOT sufficient to answer the question. B. Statement 2) alone is sufficient but statement 1) alone is NOT sufficient to answer the question. C. Both statements 1) and 2) together are sufficient to answer the question but neither statement is sufficient alone. D. Each statement alone is sufficient to answer the question. E. Statements 1) and 2) together are not sufficient to answer the question.

D.

Marshall has nickels, dimes, and quarters. If he has 4 more dimes than nickels, and 2 more nickels than quarters, what is the total value of his coins? 1) Marshall has 4 nickels. 2) Marshall has double the number of dimes compared to nickels. A. Statement 1) alone is sufficient but statement 2) alone is NOT sufficient to answer the question. B. Statement 2) alone is sufficient but statement 1) alone is NOT sufficient to answer the question. C. Both statements 1) and 2) together are sufficient to answer the question but neither statement is sufficient alone. D. Each statement alone is sufficient to answer the question. E. Statements 1) and 2) together are not sufficient to answer the question.

D.

Machine A makes 0.25 tires per minute. Machine B makes 0.3 tires per minute. Quantity A: Tires made by Machine A in 2 hours Quantity B: Tires made by Machine B in 1.5 hours

Quantity A is greater

Quantity A: Quantity B: Value of 5 quarters Value of 12 dimes

Quantity A is greater

Solution A contains 50% sulfuric acid. Solution B contains 75% sulfuric acid. A chemist wants to add the two solutions to make 100 liters of a solution that is 60% sulfuric acid. Quantity A: Liters of Solution A Required Quantity B: Liters of Solution B Required

Quantity A is greater

To make 50 gallons of 40% alcohol solution, x gallons of 30% alcohol solution and y gallons of 80% alcohol solution were mixed. Quantity A x Quantity B y

Quantity A is greater

Amber invested $1,000 at a simple annual interest rate of 25%. Quantity A: The time it takes for her initial investment to double Quantity B: 5 years

Quantity B is greater

Bob traveled 320 miles at an average speed of 40 miles per hour. Phil took 2 more hours to complete the same amount of distance as Bob. Quantity A Phil's Average Speed for the Entire Trip Quantity B 35 miles per hour

Quantity B is greater

Consider the two values below: Quantity A: Quantity B: 100 miles per hour 600,000 feet per hour

Quantity B is greater

Luke is two-thirds the age of his uncle Michael. The two have a combined age of 80. Quantity A: Micheal's current age Quantity B: Luke's age in 20 years

Quantity B is greater

Quantity A Value of 3 quarters and 5 nickels Quantity B Value of 2 quarters and 6 dimes

Quantity B is greater

Quantity A: Quantity B: 100 inches 9 feet

Quantity B is greater

To get to work, Lewis drives at a speed of 40 mph for 50 miles, and then 50 mph for another 50 miles. Quantity A: Average speed for the entire trip Quantity B: 45 mph A. Quantity A is greater. 1(9.4%) B. Quantity B is greater. 2(67.3%) C. The two quantities are equal. 3(22.4%) D. The relationship cannot be determined from the information given. 4(0.9%)

Quantity B is greater

In a high school, there are 60 fifth graders and 50 sixth graders. 50% of the fifth graders have a smartphone, while 60% of the sixth graders have a smartphone. Quantity A: Number of fifth graders with a smartphone Quantity B Number of sixth graders with a smartphone

The two quantities are equal