Question

What is the value of x?

Answer 1

R = red one.

g = green one.

b = blue one.

$\bf \begin{cases} r+g=24\\ r+b=10\\ b+g=20 \end{cases}\\\\ -------------------------------\\\\ r+g=24\implies \boxed{r}=24-g \\\\\\ r+b=10\implies \boxed{24-g}+b=10\implies b=10-24+g \\\\\\ \underline{b}=-14+g\\\\ -------------------------------$

$\bf therefore\qquad b+g=20\implies \underline{-14+g}+g=20 \\\\\\-14+2g=20 \\\\\\ 2g=34\implies g=\cfrac{34}{2}\implies g=17\qquad \begin{cases} b+g=20\\ b=20-g\\ b=20-17\\ b=3\\ ------\\ r+b=10\\ r+3=10\\ r=10-3\\ r=7 \end{cases} \\\\\\ \stackrel{7}{r}+\stackrel{b}{3}+\stackrel{17}{g}=27$

Answer 2

Red + green = 24; (1)
red + blue  = 10; (2)
blue + green = 20; (3) 

(1) - (2):
green - blue = 14;  (4)

(3) + (4):
2 * green = 34;
green = 17;

Simple substitution gives:
blue = 3;
red = 7;