Ratios, Conversions, and Rates
Given that one pound is sixteen ounces, what is the ratio of 1 pound, 4 ounces to 3 pounds, 10 ounces?
10:29
Compute 40% of 20% of 10% of 80,000.
640
What is the number of degrees in the smaller angle between the hour hand and the minute hand on a clock at 8:30?
75 degrees
What is the formula for the area of a triangle, parallelogram, and trapezoid?
Triangle - bh/2
Parallelogram - bh
Trapezoid - (a+b)h/2
The length of a rectange is three times its width. If the perimeter of the rectangle is 32 cm, what is its area?
48 cm squared
A seasonal pond in my yard has 1000 gallons of water. If water evaporates at the rate of 12.5 gallons per day and no other water is added or removed, then how much water will be in the pond after 30 days?
625 gallons
125 cups of coffee
A revolving restaurant rotates one complete revolution every 56 minutes. In the 21 minutes it takes to eat the peaches jubilee dessert, through how many degrees does the restaurant revolve?
135 degrees
If the shorter leg of a 30-60-90 triangle has a length of 10 cm, what is the length of the hypotenuse and the longer leg?
Hypotenuse - 20 cm
Longer Leg - 10√3 cm
The sum of four consecutive even integers is equal to three times the smallest number. What is the sum of the four integers?
-36
A fortnight is 14 days, and a mile is 8 furlongs. If a desert caravan travels 10 miles per day, then how many furlongs does it travel in a fortnight?
1120 furlongs
Jack had a bag of 128 apples. He sold 25% of them to Jill. Next he sold 25% of those remaining to June. Of those apples still in his bag, he gave the most shiny one to his teacher. How many apples did Jack have then?
71 apples
The angle measures of a scalene triangle are x, 2x, and 2x+15 degrees. What is the measure of the smallest angle?
33 degrees
A 25-foot ladder reaches 24 feet up the side of a building. Then the top of the ladder slides down 4 feet while the bottom slides horizontally away from the wall. How many additional feet does the bottom of the ladder slide out from the base of the building?
8 feet
Molly's father James is three years less than three times her age. How many years from now will Molly's father be twice her age if James is 33 today?
9 years
Working alone, Jamie can mow her lawn in 75 minutes. If Bob helps her, then the two can mow the lawn in 30 minutes. How long does it take Bob to mow the lawn alone?
50 minutes
Find x if 20% of x equals 12% of (x+20).
x=30
A regular polygon has interior angles measuring 179 degrees and a side length of 2 cm. Find its perimeter.
720 cm
What is the height of a STOP sign (regular octagon) whose sides are one foot long?
1+√2 feet
A hexagon and pentagon share the property that the side lengths of each are consecutive integers, and the perimeter of each is 45 cm. What is the difference in length between the short side of the pentagon and the short side of the hexagon?
2 cm
Four short-order cooks can make 24 omelets in 10 minutes. If a diner gets a to-go order for 90 omelets that need to be ready in 15 minutes, then how many cooks do they need to complete the order?
10 Cooks
Suppose Paul receives a 6% raise every year. After four such raises, what is the total percentage increase to the nearest whole percent?
26%
In a regular decagon ABCDEFGHIJ, what is the measure of angle ACB?
18 degrees
Find the length AC in regular hexagon ABCDEF if the perimeter of the hexagon is 24 cm.
4√3 cm
Kris runs half of the distance to school averaging 6 mph. He jogs the rest of the way to school averaging 4 mph, and the whole trip takes him 25 minutes. How many minutes will it take him to run the same way home if he averages 8 mph the whole way?
15 minutes