Solve the system of equations to find the values of x, y and z: xy/(x+y)=1/2, yz/(y+z)=1/3, zx/(z+x)=1/7
If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.
A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?
Four jewellers possessing respectively eight rubies, ten
saphires, a hundred pearls and five diamonds, presented, each from
his own stock, one piece to each of the rest in token of regard;
and they thus became owners of stock of precisely equal value. Tell
me the prices of their gems and the values of their stocks.
[This problem comes from Lilavati , a standard work on
Hindu mathematics written by Bhasakaracharyya, who lived in the
twelfth century of the Christian era. The book is written as
instruction for a young and beautiful woman called Lilavati and it
is thought that she was