Determine x,y,z if x/2=y/3=z/5 and x+y+z=20

Given that:

x/2 = y/3 =
z/5..........(1)

x+ y + z =
20.........(2)

From (1) we will rewrite the numbers as
functions of x.

==> x/2 =
y/3

==> y= (3/2)x
............(3)

==> x/2 =
z/5

==> z = (5/2)x
.............(4)

Now we will substitute (3) and (4) into
(2).

==> x + y + z =
20

==> x + (3/2)x + (5/2)x =
20

==> (2+ 3+5)/2 x =
20

==> 10/2 x =
20

==> 5x =
20

==> x = 20/5 =
4

==> y= (3/2)x = 3/2 * 4 =
6

==> z= (5/2)x = 5/2 * 4 =
10

Then the numbers are: ( x, y, z) = ( 4, 6,
10)