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Real(ly) Numbers

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

Overturning Fracsum

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

Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

Leonardo's Problem

Age 14 to 18 Challenge Level:
You have to create your own equations here. Choose letters for the total sum, and for the number of coins each person grabbed. Then express the given information in equations and finally solve your set of simultaneous equations.