I found a stone but did not weigh it. After I added a seventh, and then added an eleventh of the result, I weighed it and found it weighed $1$ mina. What was the original weight of the stone?
The answer given on the cuneiform tablet is ${\frac 23}$ mina, $8$ sheqel, and $22{\frac 12}$ se, where $1$ mina = $60$ sheqel, and $1$ sheqel = $180$ se.
In ancient Egypt, knowing how to solve word problems was a highly prized secret. The Rhind Papyrus (ca. 1850 B.C.) contains many such problems. Problem 32 in the Papyrus states
A quantity, its third, its quarter, added together become $2$. What is the quantity?
The answer in Egyptian notation is $1 + \overline 4$ + $\overline {76}$, where the bar indicates "reciprocal," much like our notation $4^{-1}$.
The Greek mathematician Diophantus (ca. 250 A.D.) wrote the book Arithmetica, which contains many word problems and equations. The Indian mathematician Bhaskara (12th century A.D.) and the Chinese mathematician Chang Ch'iu-Chien (6th century A.D.) also studied and wrote about equations. Of course, equations continue to be important today.
If a rooster is worth $5$ coins, a hen $3$ coins, and three chicks together one coin, how many roosters, hens, and chicks, totaling $100$, can be bought for $100$ coins?