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Problems from Another Time

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

One says that 10 garments were purchased by two men at a price of 72 dirhams. The garments varied in value. The price of each garment of one man is 3 dirhams more than the price for each garment of the other. How many garments did each man buy?
Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
There are two columns in the ruins of Persepolis left standing upright; one is 70 ft. above the plane, and the other 50 ft;
What is the sum of the reciprocals of the triangular numbers?
If 12 cattle eat up 3 1/3 acres of meadow in 4 weeks and 21 cattle eat up 10 acres of exactly similar meadow in 9 weeks, how many cattle shall eat up 36 acres in 18 weeks? (Hint: The grass continues to grow.)
Suppose the area of an equilateral triangle be 600. The sides are required.
If a ball 6 inches in diameter weighs 32 lbs, what will be the weight of a ball 3 inches in diameter?
A certain gentleman ordered that 90 measures of grain were to be transported from his house to another, 30 leucas distant.
Find the two numbers such that multiplying one by the other makes 8 and the sum of their squares is 27
Given a pendulum as shown. The height of the pendulum is two units and its horizontal width is 2 units. What is the area of the pendulum?

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