A store is offering a 20% discount on all books. If a book originally costs $25, what is the final price after the discount?
The discount amount is $25 x 0.20 = $5. The final price is $25 - 5 = $20.
If 5x+3=18, what is the value of x?
Subtract 3 from both sides: 5x=15. Divide by 5: x=3.
A jacket is on sale for $45. This price represents a 25% discount from the original price. What was the original price of the jacket?
The sale price is 75% of the original price. Let P be the original price. 0.75 x P=45. P=45/0.75=60.
If a=3b and c=2a, what is c in terms of b?
We know c=2a and a=3b. Substitute the value of a into the second equation: c=2(3b)=6b.
A car travels at an average speed of 50 miles per hour for 4 hours. How far does the car travel?
Distance = Speed x Time. Distance = 50 x 4=200 miles.
What is the value of 1/2+1/3+1/4?
Find a common denominator, which is 12. 1/2=6/12, 1/3=4/12, 1/4=3/12. The sum is (6+4+3)/12=13/12.
A bakery sells two types of muffins: chocolate and blueberry. If the ratio of chocolate muffins to blueberry muffins sold is 5:3, and the bakery sells a total of 72 muffins, how many chocolate muffins were sold?
The total ratio parts are 5+3=8. The value of one part is 72/8=9. The number of chocolate muffins is 5x9=45.
What is the area of a circle with a diameter of 10 cm?
The radius is half the diameter, so r=10/2=5 cm. The area of a circle is π r^2. Area = π(5^2)=25π cm^2.
A company's revenue increased by 10% in the first year and then increased by 20% in the second year. What was the net percentage increase in revenue over the two-year period?
Let the original revenue be R. After year one, it is Rx1.10=1.1R. After year two, it is 1.1Rx1.20=1.32R. The net increase is 0.32R, which is 32%.
If m is a positive integer, which of the following expressions is always even?
A positive integer multiplied by 2 will always result in an even number.
If x is a prime number and y is an odd number, which of the following must be odd?
A prime number can be even (2) or odd (3, 5, etc.). An odd number multiplied by 2 is always even. Adding an odd number (y) to an even number will always result in an odd number.
A worker can complete a task in 5 hours. Another worker can complete the same task in 8 hours. If they work together, how long will it take them to complete the task?
The first worker completes 1/5 of the task per hour, and the second completes 1/8. Together, their rate is 1/5+1/8=8/40+5/40=13/40. The time to complete the task is 1/(13/40)=40/13 hours, or approximately 3.07 hours. 0.07x60 approx minutes. The closest answer is 3 hours and 5 minutes.
The average of five numbers is 10. If one of the numbers is removed, the average of the remaining four numbers is 8. What number was removed?
The sum of the five numbers is 5x10=50. The sum of the remaining four numbers is 4x8=32. The removed number is the difference: 50-32=18.
A store sold 150 items on Monday. On Tuesday, they sold 20% more items than on Monday. How many items did they sell on Tuesday?
The number of items sold on Tuesday is 150x1.20=180.
A rectangular garden is 12 meters long and 8 meters wide. If a path 2 meters wide is built around the outside of the garden, what is the area of the path?
The area of the garden is 12x8=96 m^2. The new dimensions including the 2-meter path are (12+4) m by (8+4) m, which is 16 m by 12 m. The total area is 16x12=192 m^2. The area of the path is the total area minus the garden's area: 192-96=96 m^2.
If x>0 and x^2=81, what is the value of x?
The square root of 81 is 9. Since the question specifies x>0, the answer is positive 9.
What is 0.05% of 200?
First, convert 0.05% to a decimal by dividing by 100: 0.05/100=0.0005. Then multiply by 200: 0.0005x200=0.1.
A box contains 5 red balls, 3 blue balls, and 2 green balls. If a ball is randomly selected from the box, what is the probability that it is not red?
The total number of balls is 5+3+2=10. The number of balls that are not red is 3+2=5. The probability is the number of favorable outcomes over the total number of outcomes: 5/10=1/2.
If x-y=4 and 2x+y=11, what is the value of x?
You can solve this with a system of equations. Add the two equations together: (x-y)+(2x+y)=4+11. 3x=15. x=5.
A school has 400 students. If 60% of the students are boys, and 25% of the boys play a sport, how many boys play a sport?
The number of boys is 400x0.60=240. The number of boys who play a sport is 240x0.25=60.
What is the sum of all integers from 1 to 50, inclusive?
Use the formula for the sum of an arithmetic series: Sum=n(a1+an)/2, where n is the number of terms, a1 is the first term, and an is the last term. Sum = 50(1+50)/2=50(51)/2=25x51=1,275.
A cube has a side length of 5 cm. What is the volume of the cube?
The volume of a cube is side length cubed. Volume = 5^3=5x5x5=125 cm³.
If x=-3, what is the value of x²-2x+1?
Substitute x=-3 into the expression: (-3)^2-2(-3)+1. This becomes 9-(-6)+1=9+6+1=16.
A certain car consumes 1 gallon of gas for every 30 miles it travels. How many gallons of gas will the car need to travel 240 miles?
Divide the total distance by the miles per gallon: 240/30=8 gallons.
What is the least common multiple of 12 and 18?
Find the prime factors of each number. 12=2^2x3. 18=2x3^2. The LCM is found by taking the highest power of each prime factor: 2^2x3^2=4x9=36.
If a shirt is bought for $40 and sold for $50, what is the percent profit?
Profit is calculated as Selling Price - Cost. Profit = $50 - 40 = $10. The percent profit is (Profit / Cost) x100%. Percent profit = (10/40)x100%=0.25x100%=25%.
The circumference of a circle is 16π. What is the radius of the circle?
The formula for the circumference of a circle is C=2π r. Given C=16π, we have 16π=2π r. Divide both sides by 2π to find r=8.
What is the value of (5³)x(5²)?
When multiplying exponents with the same base, you add the powers. 5^3x5^2=5^(3+2)=5^5.
A train leaves a station at 1:00 PM and arrives at its destination at 4:30 PM. If the distance traveled is 210 miles, what is the average speed of the train in miles per hour?
The train's travel time is from 1:00 PM to 4:30 PM, which is 3.5 hours. Average speed = Distance / Time. Speed = 210/3.5=60 mph.
If x and y are positive integers, and x+y=10, what is the maximum possible value of xx y?
To maximize the product of two numbers with a fixed sum, the numbers should be as close as possible. The two positive integers whose sum is 10 and are closest to each other are 5 and 5. Their product is 5x5=25.
Share your Results:
For answer key click me.
