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Problems from Another Time

Individual problems from throughout mathematics history, as well as articles that include problem sets for students.

The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11″ and a second side, 19″. Find the lengths of the sides of the second triangle.
A boy gives 11 coins of equal denomination to a man, and the man finds that their total value in yen is 4 less than his age.
What is the value of X...
There were two men, of whom the first had 3 small loaves of bread and the other, 2.
On a day in spring a boy has gathered cherry blossoms under a cherry tree. Nearby a poet is reading some of his poems aloud. As he reads, the boy counts out the cherry blossoms, one blossom for each word of a poem.
What proportions of sugar at 8 cents, 10 cents and 14 cents per pound, will compose a mixture worth 12 cents per pound?
Given four integers where if added together three at a time their sums are: 20, 22, 24, and 27. What are the integers?
Fibonacci gave a practical rule for approximating the area of an equilateral triangle.
In the figure at the left, if the radii of each inscribed circle is 1, what are the dimensions of the bounding rectangle?
The dimensions of a rectangular box in inches are expressed by three consecutive numbers. The surface of the box is 292 square inches. Find the dimensions.

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