Applied Math Flashcards

A stack of bricks is 3 1/2 feet high. If each brick is 1 3/4 inches high, how many bricks are in the stack?

Answer: 24

First, ensure all measurements are in the same unit. Convert the stack height from feet to inches: 3 1/2 feet = 3.5 feet × 12 inches/foot = 42 inches. Each brick is 1 3/4 inches (or 1.75 inches) high. To find the number of bricks, divide the total stack height by the height of one brick: 42 inches ÷ 1.75 inches = 24 bricks.

A book regularly sells for $28. If the book is on sale for "20% off", how much is the sales price of the book?

Answer: $22.40

To find the sales price, first calculate the discount amount. A 20% discount on a $28 book is 0.20 × $28 = $5.60. Then, subtract the discount from the regular price: $28.00 - $5.60 = $22.40. This is the sales price of the book.

A scale on a map says that 1 inch represents 60 miles. If the distance between two points on the map is 2 1/2 inches, how many miles are between the two points?

Answer: 150

The map scale states that 1 inch represents 60 miles. To find the actual distance between two points that are 2 1/2 inches apart on the map, multiply the map distance by the scale factor. So, 2.5 inches × 60 miles/inch = 150 miles. This is the actual distance between the two points.

A car has a 15 gallon gas tank. If a car gets 32 miles per gallon and travels 384 miles, how much gas will be left in the tank?

Answer: 3

To find the gas remaining, first determine how much gas was used by dividing the total miles traveled (384) by the car's miles per gallon (32), which equals 12 gallons. Then, subtract the used gas (12 gallons) from the tank's full capacity (15 gallons). This calculation shows that 3 gallons of gas will be left in the tank.

A man's hourly wage increased from $12.50 to $13.50. What percent raise did he get?

Answer: 8%

First, calculate the amount of the raise by subtracting the original wage from the new wage ($13.50 - $12.50 = $1.00). To find the percent raise, divide the raise amount ($1.00) by the original wage ($12.50), which gives 0.08. Multiply this decimal by 100 to convert it to a percentage, resulting in an 8% raise.

If you pay $22.90 for a DVD that includes a 7% sales tax, what is the price of the DVD before the sales tax?

Answer: $21.40

The total price paid ($22.90) represents the original price plus the 7% sales tax. This means $22.90 is 107% (or 1.07) of the original price. To find the price before tax, divide the total price by 1.07. Therefore, $22.90 / 1.07 equals $21.40, which is the DVD's price before sales tax.

A toll is $2 for a car and the driver and 75 cent for each additional passenger. If the toll comes to $4.25, how many total people are in the car?

Answer: 4

First, subtract the base toll for the car and driver ($2.00) from the total toll paid ($4.25), leaving $2.25. This remaining amount covers the additional passengers. Divide $2.25 by the cost per additional passenger ($0.75) to find there are 3 additional passengers. Adding the initial driver to these 3 passengers gives a total of 4 people in the car.

A plane left San Francisco at 6:15 pm PST and arrived in Philadelphia at 2:45 am EST. How long was the flight?

Answer: 5 1/2 hours

First, convert the departure time from PST to EST. San Francisco (PST) is 3 hours behind Philadelphia (EST), so 6:15 pm PST is 9:15 pm EST. Next, calculate the duration from 9:15 pm EST to 2:45 am EST. This period spans 5 hours and 30 minutes, meaning the flight was 5 1/2 hours long.

Carpet costs $3 per square yard. The room that will be carpeted is 12 feet x 18 feet. How much will the carpet cost?

Answer: $72

First, calculate the area of the room in square feet: 12 feet * 18 feet = 216 square feet. Since carpet is priced per square yard and 1 yard equals 3 feet, 1 square yard equals 9 square feet. Convert the room's area to square yards by dividing 216 by 9, which gives 24 square yards. Finally, multiply the total square yards by the cost per square yard ($3) to get the total cost of $72.

A product originally costs $125. If the product goes on sale for 20% off, and then goes on sale for an additional 30% off, what is the price of the product?

Answer: $70

First, calculate the price after the initial 20% discount. 20% of $125 is $25, so the price becomes $125 - $25 = $100. Next, apply the additional 30% discount to this new price of $100. 30% of $100 is $30, so the final price is $100 - $30 = $70.

There are 12 women, 8 teenagers, and 5 teenage women in a dinner group of 20. How many men who are not teenagers are present at the party?

Answer: 5

First, determine the number of people who are either women or teenagers. There are 12 women, and 8 teenagers, with 5 being both. So, 12 (women) + (8-5) (teenagers who are not women) = 12 + 3 = 15 people who are either women or teenagers. Since the total group is 20 people, subtract these 15 people from the total to find the number of men who are not teenagers: 20 - 15 = 5.

What is the volume of the box shown?

Answer: 6820 cubic inches

To calculate the volume of a rectangular box, multiply its length, width, and height. Assuming the dimensions provided in the accompanying image are 22 inches, 20 inches, and 15.5 inches, the calculation is 22 * 20 * 15.5. This multiplication yields a volume of 6820 cubic inches.

What time period comes the closest to 5.67 hours?

Answer: 5 hours, 40 minutes

To convert the decimal part of the hours into minutes, multiply the decimal (0.67) by 60 minutes per hour. This calculation results in 40.2 minutes. Therefore, 5.67 hours is equivalent to 5 hours and 40.2 minutes, which is closest to 5 hours, 40 minutes.

Which of the following best sums up the right triangle's sides?

Answer: 8 units, 15 units 17 units

For a set of side lengths to form a right triangle, they must satisfy the Pythagorean theorem: a² + b² = c², where 'c' is the longest side (hypotenuse). Testing the given options, only 8² + 15² = 64 + 225 = 289, and 17² = 289. Since 289 = 289, the sides 8 units, 15 units, and 17 units form a right triangle.

A contractor works four jobs and makes $563, $612, $890, and $392 in one month. How much did the contractor make on these four projects, on average?

Answer: $2,500

To find the total amount the contractor made, sum the earnings from all four jobs: $563 + $612 + $890 + $392 = $2457. Given the options, the question likely asks for this total amount rounded to the nearest hundred. Rounding $2457 to the nearest hundred yields $2500.

The number 8835 was rounded by Clair to the nearest hundred. This amount was rounded to the nearest thousand by Steve. What made the two rounded numbers different from one another?

Answer: 200

Clair rounded 8835 to the nearest hundred. Since the tens digit (3) is less than 5, she rounded down to 8800. Steve rounded 8835 to the nearest thousand. Since the hundreds digit (8) is 5 or greater, he rounded up to 9000. The difference between their rounded numbers is 9000 - 8800, which equals 200.