Выразим x через y:
x : y = 4 : 9
9x = 4y
$x = \frac{4}{9}y$;
Выразим z через y:
$y : z = 15 : 2\frac{2}{3}$
$15z = \frac{8}{3}y$
$z = \frac{8}{3}y : 15$
$z = \frac{8}{3}y : \frac{1}{15}$
$z = \frac{8}{45}y$;
x + y + z = 219, заменим x и z:
$\frac{4}{9}y + y + \frac{8}{45}y = 219$
$\frac{20 + 45 + 8}{45}y = 219$
$\frac{73}{45}y = 219$
$y = 219 : \frac{73}{45}$
$y = 219 * \frac{45}{73}$
y = 3 * 45
y = 135, тогда:
$x = \frac{4}{9}y = \frac{4}{9} * 135 = 4 * 15 = 60$;
$z = \frac{8}{45}y = \frac{8}{45} * 135 = 8 * 3 = 24$.
219 = 60 + 135 + 24