Area is Perimeter

The value of a square's perimeter in inches is the same as the value of its area in square inches. What is the length of it's side?

Aspect ratio

Movies and the screens we view them on typically come in two formats. Standard format has a 3:4 aspect ratio, meaning that the picture height is ³/₄ of the picture width. Widescreen format has a 9:16 aspect ratio, so the picture height is ⁹/₁₆ of the picture width. A widescreen movie shown on a standard screen has two horizontal black bars, one above and one below the picture. Likewise, a standard movie shown on a widescreen screen has vertical black bars on the sides. What percent of the viewing area is lost to the black bars when viewing a widescreen movie on a standard screen? How about when viewing a standard movie on a widescreen screen?

Perimeter is Area

A rectangle is 3 inches longer than it is wide. The value of it's perimeter in inches is the same as the value of its area in square inches. What is the width of the rectangle?

Find a Line

Find the equation of a line that passes through −3 on the y axis and 2 on the x axis.

Odd Numbers

It's been a hectic month. I am now employed again, and have had little time for word problems. However, here's a good brain teaser.

A number is "singly even" if it can be evenly divided by 2 but not by 4. The numbers 2, 6, 10, 14, 18, ... are all "singly even." Show that the sum of a sequential series of odd numbers (e. g., 9 + 11 + 13 + 15) must be odd or divisible by 4; it cannot be "singly even."

Twice and Thrice

The sum of two integers is twice their difference. Their product is three times their difference. What are the two integers?

Easy Does It

The ratio of two numbers is twice their sum, and their difference is zero. What are the two numbers?

Another Angle

The ratio of ∠ABC to ∠CDE is 4:5. What is the measure of ∠CBD?

Russian Mathematicians Again

"Well," said Pavel. "I have two sons closer to one another in age than your two girls, though still some years apart. It is, perhaps, a coincidence that the product of their ages is exactly six times the sum."
"Ah," said Grigori. "Thank you for letting me know their ages."
How old are Pavel's sons?

Russian Mathematicians

Two Russian mathematicians, Pavel and Grigori met at a conference in Vienna where the following conversation ensued:
Pavel: Grigori! It's been such a long time. How are you?
Grigori: Fine, Pavel. And you? I hope you are well.
Pavel: Indeed, I am. It must be fifteen years. You have children now, I believe.
Grigori: Yes two darling girls.
Pavel: And how old are they?
Grigori: Well, it's curious. The product of their ages this year is just three times the sum.
Pavel: I'm sorry, Grigori, but I still can't work out their ages.
Grigori: Of course. I forgot to tell you how excited little Nikki was when Pavla was born.
Pavel then knew the ages of the two girls. What are they? How old was Nikki when Pavla was born?

Stopping Distance

At 35 mph a car has a stopping distance of about 50 feet. The stopping distance is directly proportional to the kinetic energy of the car, which is proportional to (mv²)/2, where m is the mass of the car and v is its velocity. How many more feet will be required to stop at 40 mph?

Kinetic Energy

A Ford Taurus with an 80-kg driver has a mass of approximately 1732 kg. The kinetic energy of the car and driver can be calculated from the formula E = (mv²)/2, where m is the mass of the car and driver, and v is the velocity. The resultant energy is expressed in joules (J). Find the kinetic energy of the car and driver at 27 m/sec.

Sum Product

The product of two integers is equal to their sum. What are the two integers? Prove that there are only two solutions.

More Difference

The sum of two numbers is ten more than their difference. The difference is 7. What are the two numbers?

Two Numbers

The product of two whole numbers is three times their sum, and their sum is twice their difference. What are the two numbers?