- A rope is 50 meters long. Pieces of the rope measuring 2 feet 6 inches are cut from it. How many full pieces can be cut from the rope? (1 meter ≈ 3.28 feet)
Answer: 65
First, convert all measurements to a single unit, such as feet. The length of the rope is 50 meters × 3.28 feet/meter = 164 feet. The length of each piece to be cut is 2 feet 6 inches. Since 6 inches is 0.5 feet, each piece is 2.5 feet long. Finally, divide the total length of the rope by the length of one piece: 164 feet / 2.5 feet/piece = 65.6 pieces. Since only full pieces can be cut, the answer is 65.
- A carpenter has a board that is 4 yards, 2 feet, and 5 inches long. She cuts off a piece that is 7 feet and 8 inches long. What is the length of the remaining board in inches?
Answer: 81 inches
First, convert both lengths entirely to inches. Original board: 4 yards = 4 × 3 feet/yard = 12 feet. Total feet = 12 + 2 = 14 feet. Total inches = (14 feet × 12 inches/foot) + 5 inches = 168 + 5 = 173 inches. Cut piece: (7 feet × 12 inches/foot) + 8 inches = 84 + 8 = 92 inches. Subtract the cut piece from the original length: 173 inches - 92 inches = 81 inches.
- A package weighing 3.5 kilograms is shipped internationally. If the shipping cost is based on weight in pounds, what is the weight of the package in pounds and ounces? (1 kg ≈ 2.2 lbs; 1 lb = 16 oz)
Answer: 7 pounds, 11 ounces
First, convert kilograms to pounds: 3.5 kg × 2.2 lbs/kg = 7.7 lbs. The weight is 7 full pounds with a remainder of 0.7 pounds. Convert the remainder to ounces: 0.7 lbs × 16 oz/lb = 11.2 ounces. Thus, the weight is approximately 7 pounds, 11 ounces.
- A temperature reading is 25° Celsius. To convert Celsius to Fahrenheit, the formula is F = (9/5)C + 32. A change of 1° Celsius is equivalent to a change of how many degrees Fahrenheit?
Answer: 1.8° F
This question tests the understanding of a conversion formula as a rate of change, not just a single conversion. The formula F = (9/5)C + 32 is a linear equation. The coefficient (9/5) represents the rate of change, which equals 1.8. This means that for every 1-unit increase in C, F increases by 1.8. Therefore, a change of 1° Celsius is equivalent to a change of 1.8° Fahrenheit.
- A swimming pool is being filled at a rate of 500 gallons per hour. How many quarts per minute is this filling rate? (1 gallon = 4 quarts)
Answer: 33.3 quarts per minute
This requires converting both volume and time. First, convert gallons to quarts: 500 gallons/hour × 4 quarts/gallon = 2,000 quarts/hour. Next, convert the rate from 'per hour' to 'per minute' by dividing by 60 minutes/hour: 2,000 quarts/hour / 60 minutes/hour ≈ 33.3 quarts per minute.
- A field is 100 meters long. An athlete runs the length of the field and back (a total of 200 meters) in 25 seconds. What was the athlete's average speed in kilometers per hour?
Answer: 28.8 km/h
First, calculate the athlete's speed in meters per second: Speed = Distance / Time = 200 meters / 25 seconds = 8 m/s. To convert m/s to km/h, multiply by the conversion factor 3.6 (which is 3600 seconds/hour divided by 1000 meters/km). Speed in km/h = 8 m/s × 3.6 = 28.8 km/h.
- A laboratory experiment requires 150 milligrams of a chemical for each of 20 samples. If the chemical is sold in 5-gram containers, what is the minimum number of containers that must be purchased?
Answer: 1
First, calculate the total amount of chemical needed: 150 mg/sample × 20 samples = 3,000 mg. Next, convert this total from milligrams to grams, knowing that 1 gram = 1,000 milligrams: 3,000 mg / (1,000 mg/gram) = 3 grams. Since the chemical is sold in 5-gram containers and only 3 grams are needed, one container is sufficient.
- A high-speed train travels at 320 kilometers per hour. How many meters does the train travel in 15 seconds?
Answer: 1,333 meters
First, convert the speed from kilometers per hour to meters per second. 1 km = 1000 m and 1 hour = 3600 seconds. Speed = (320 km/hr) × (1000 m/km) / (3600 s/hr) = 320,000 / 3,600 m/s ≈ 88.89 m/s. Now, calculate the distance traveled in 15 seconds: Distance = Speed × Time = 88.89 m/s × 15 s ≈ 1,333 meters.
- A rectangular room has an area of 162 square feet. If carpeting is sold by the square yard, how many square yards of carpet are needed to cover the floor?
Answer: 18
To convert square feet to square yards, one must know the relationship between feet and yards. Since 1 yard = 3 feet, it follows that 1 square yard = (3 feet) × (3 feet) = 9 square feet. To find the area in square yards, divide the area in square feet by 9: 162 square feet / 9 square feet per square yard = 18 square yards.
- A garden hose has a diameter of 5/8 inch. Which of the following lengths is closest to this diameter? (1 inch = 2.54 centimeters; 1 centimeter = 10 millimeters)
Answer: 16 millimeters
First, convert the fraction to a decimal: 5/8 = 0.625 inches. Next, convert inches to centimeters: 0.625 inches × 2.54 cm/inch ≈ 1.5875 cm. Finally, convert centimeters to millimeters: 1.5875 cm × 10 mm/cm = 15.875 mm. The closest value among the choices is 16 millimeters.
- A construction project is estimated to require 2,500 person-hours to complete. If a team of 8 people works on the project for 40 hours per week each, how many full weeks will it take to complete the project?
Answer: 8
First, calculate the total person-hours the team works per week: 8 people × 40 hours/person = 320 person-hours per week. Next, divide the total required person-hours by the team's weekly output: 2,500 person-hours / 320 person-hours/week ≈ 7.8125 weeks. Since the project must be completed, it will take the entirety of the 8th week. Therefore, 8 full weeks are required.
- A bottle contains 750 milliliters of wine. A restaurant serves this wine in glasses that hold 1.5 deciliters. How many full glasses can be served from one bottle?
Answer: 5
This problem involves converting between metric units of volume. First, make the units consistent. We know that 1 deciliter (dL) = 100 milliliters (mL). Convert the glass size to milliliters: 1.5 dL × 100 mL/dL = 150 mL. Now, divide the total volume of wine in the bottle by the volume of one glass: 750 mL / 150 mL/glass = 5 glasses.
- A landscaper needs to order 5 cubic yards of soil for a garden bed. The soil is delivered in bags containing 2.5 cubic feet each. How many bags must be ordered?
Answer: 54
First, convert the total soil needed from cubic yards to cubic feet. Since 1 yard = 3 feet, 1 cubic yard = (3 feet)³ = 27 cubic feet. Total soil needed: 5 cubic yards × 27 cubic feet/yard = 135 cubic feet. Next, divide the total cubic feet needed by the volume per bag: 135 cubic feet / 2.5 cubic feet/bag = 54 bags.
- A runner maintains a pace of 6 miles per hour. Approximately how many feet per second is this pace? (1 mile = 5,280 feet)
Answer: 8.8 feet per second
This is a multi-step unit conversion. First, convert miles to feet and hours to seconds. Rate = (6 miles/hour) × (5,280 feet/mile) / (3,600 seconds/hour). Numerator: 6 × 5,280 = 31,680 feet. Denominator: 1 hour = 60 minutes × 60 seconds/minute = 3,600 seconds. The rate is 31,680 feet / 3,600 seconds ≈ 8.8 feet per second.
- One can of paint covers 400 square feet. A rectangular wall is 8 yards long and 10 feet high. How many cans of paint are needed to apply two coats to the wall?
Answer: 2
First, convert the wall's length to feet: 8 yards × 3 feet/yard = 24 feet. Calculate the area of the wall: 24 feet × 10 feet = 240 square feet. For two coats, the total area to be painted is 240 sq ft × 2 = 480 square feet. Finally, determine the number of cans needed by dividing the total area by the coverage per can: 480 sq ft / 400 sq ft/can = 1.2 cans. Since you cannot buy a fraction of a can, you must purchase 2 cans.
- An aquarium tank in the shape of a rectangular prism is 90 cm long, 50 cm wide, and 60 cm high. If the tank is filled with water, what is the mass of the water in kilograms? (1 L of water has a mass of 1 kg; 1 L = 1,000 cm³)
Answer: 270 kg
First, calculate the volume of the tank in cubic centimeters: Volume = 90 cm × 50 cm × 60 cm = 270,000 cm³. Next, convert the volume from cubic centimeters to liters: 270,000 cm³ / 1,000 cm³/L = 270 L. Since 1 liter of water has a mass of 1 kilogram, the mass of the water is 270 kilograms.
- A cookie recipe calls for 8 fluid ounces of milk. A baker has a 1-liter bottle of milk. Approximately how many full recipes can the baker make with this bottle? (1 liter ≈ 33.8 fluid ounces)
Answer: 4
First, use the given conversion to find the total amount of milk available in fluid ounces: 1 liter is approximately 33.8 fluid ounces. Next, divide the total amount of milk by the amount required per recipe: 33.8 fl oz / 8 fl oz/recipe ≈ 4.225 recipes. Since the question asks for the number of full recipes, we must truncate the decimal, meaning the baker can make 4 full recipes.
- A roll of fabric is 25 yards long. A dressmaker needs to cut pieces that are each 75 centimeters long to make sashes. How many full sashes can be cut from the roll? (1 yard = 36 inches; 1 inch = 2.54 cm)
Answer: 30
First, find the total length of the fabric in centimeters. Convert yards to inches: 25 yards × 36 inches/yard = 900 inches. Then convert inches to centimeters: 900 inches × 2.54 cm/inch = 2,286 cm. Now, divide the total length by the length needed per sash: 2,286 cm / 75 cm/sash ≈ 30.48 sashes. Since only full sashes can be made, the dressmaker can cut 30 sashes.
- A patient needs to take 500 micrograms of a vitamin every day. The vitamin is available in tablets that contain 0.25 milligrams. How many tablets should the patient take per day?
Answer: 2 tablets
First, make the units consistent. We know 1 milligram (mg) = 1,000 micrograms (mcg). Convert the tablet strength to micrograms: 0.25 mg × 1,000 mcg/mg = 250 mcg. Now, divide the required daily dose by the strength of one tablet: 500 mcg / 250 mcg/tablet = 2 tablets.
- A rectangular container has inside dimensions of 20 centimeters, 30 centimeters, and 40 centimeters. What is its volume in liters, given that 1 liter is equal to 1,000 cubic centimeters?
Answer: 24 liters
First, calculate the volume of the container in cubic centimeters by multiplying its dimensions: Volume = 20 cm × 30 cm × 40 cm = 24,000 cm³. Next, convert cubic centimeters to liters using the given conversion factor: 24,000 cm³ / (1,000 cm³/liter) = 24 liters.
