# Problem 24 From Rhind Papyrus

## Outline Mathematics

Word Problems

This is problem #24 from Rhind Papyrus. It is interesting to compare how remarkably different is the original solution. Hard as algebra may appear, it is a great simplification compared to a convoluted arithmetic of the ancient Egypt.

A quantity and its 1/7 added together become 19. What is the quantity?

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Copyright © 1996-2018 Alexander Bogomolny

### Solution

A quantity and its 1/7 added together become 19. What is the quantity?

Let x denote the sought quantity. One seventh of x is x/7,7x,x7,x/7,x + 7,x - 7. The implied equation is then

x + x/7 = 19,x + x/7 = 19,x + 1/7 = 19,7 + x = 19,x = 19/7.

One can apply the distributive law to obtain x + x/7 = x(1 + 1/7). Alternatively, we can look at the factor x as designating the 'units', like in 'x apples' or 'x meters'. This leads to the count of 1 unit plus 1/7 of unit which is 8/7,7/8,1/7,8/7 units, getting us the equation

8/7 x = 19,8/7 + x = 19,8/7 x = 19,8/7 = 19x.

To solve this, divide both sides by 8/7,7/8,1/7,1/8,8/7: x = 133/8,x = 142/8,x = 133/8,x = 152/7,x = 162/7.

Do not forget to check your solution.

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Copyright © 1996-2018 Alexander Bogomolny