Of two identical barrels, one is half full and one is two-thirds full. One quarter of the liquid in the second barrel is poured into the first. The first barrel now contains 25 more gallons of liquid than the second. Find the capacity in gallons of one of the barrels.

## Set 18

## Cube Made of Bricks

Can a solid cube 1 foot on a side be constructed from bricks measuring 2″ x 4″ x 8″? Show that your answer is correct.

## Area of Obtuse Triangle

In an obtuse triangle, the degree measure of one of the acute angles is 45°, and the length of the shortest altitude is 5 inches. If the perimeter of this triangle is 30 + 5√2 inches, find in square inches the area of the triangle.

## Pentagon Area

A regular pentagon has side 10. Find the area of the pentagon.

## Distance in Cross

Here is a cross composed of five congruent squares. If the distance *x* = 10, find the area of the cross.

## Numerical Log Problem

If *a* = log_{8}225 and *b* = log_{2}15, then what’s *a* in terms of *b*?

*a*=*b*/2*a*= 2*b*/3*a*=*b**b*=*a*/2*a*= 3*b*/2

## Wealth Redistribution

The kingdom of Syldavia has five economic classes. Feeling one day that there is too great a disparity among the wealth of the classes, the King asks his Finance Minister to devise a plan to redistribute the wealth of the classes. The FM proposes that the wealth of the top two classes be averaged, then the wealth of classes 2 and 3 be averaged, then the wealth of classes 3 and 4 be averaged, and finally that the wealth of classes 4 and 5 be averaged—a four-step process. The King likes the sound of the plan, but suggests that the progression should be from the lowest classes upwards. (In either case, the result will be a four-class system.) Which of the two plans should the lowest class prefer? Why?

## Radical of Year of Birth

Stella’s grandfather was born during the 19th century. The square root of the year he was born, plus the square root of the year that Stella’s cousin Elspeth was born, equals the age of Stella’s grandfather when he died. So in what year did her gramps die, how old was he at his death, and how old is Elspeth now?

## Train Roars Through Station

An express train roars through the train station, taking 5 seconds to pass a waiting passenger, and 19 seconds to clear the whole station. The platform is 280 meters long. How long is the train, and at what speed is it moving?

## Snow Tires

On Orville’s ski trip, he went up with regular tires and the odometer said he drove 450 miles. He came back with snow tires on and the odometer said 440 miles. Find, to the nearest hundredth of an inch, the increase in radius of the snow tires if the radius of his regular tires was exactly 15 inches.