How to find 3 unknowns behind proportions?

Question

Mathematics

The purpose of such a plan There is a certain number, let it be 1000, which is calculated as the sum of three unknowns x, y, z (x + y + z = 1000). We only know the proportions between these unknowns: x : y = 2 : 3 and y : z = 2 : 3. How can we find all the unknowns? Can you explain how such problems are solved?

Answer 1

Easily. Through proportions, all variables must be reduced to one, possibly introduced artificially, then the first equation will be linear with one variable.

y/z = 2/3 => y = (2/3)z
x/y = 2/3 => x = (2/3)y = (4/9)z
(4/9)z+(2/3)z+z = 1000
(19/9)z = 1000
z = 9000/19
y = 6000/19
x = 4000/19