Answer:
[tex]9\ oz[/tex] ---> red tone
[tex]6\ oz[/tex] ----> gray tone
[tex]5\ oz[/tex] -----> brown tone
Step-by-step explanation:
Let
x-----> the number of ounces of red tone
y----> the number of ounces of gray tone
z---> the number of ounces of brown tone
we know that
[tex]x+y+z=20[/tex] -----> equation A
[tex]\frac{x}{y}=\frac{(9/8)}{(3/4)}=1.5[/tex]
[tex]x=1.5y[/tex] -----> equation B
[tex]\frac{x}{z}=\frac{(9/8)}{(5/8)}=1.8[/tex]
[tex]x=1.8z[/tex] -----> equation C
[tex]\frac{y}{z}=\frac{(3/4)}{(5/8)}=1.2[/tex]
[tex]y=1.2z[/tex] -----> equation D
substitute equation D and equation equation C in equation A
[tex]1.8z+1.2z+z=20[/tex]
solve for z
[tex]4z=20[/tex]
[tex]z=5\ oz[/tex] -----> brown tone
Find the value of x
[tex]x=1.8z[/tex] -----> [tex]x=1.8(5)=9\ oz[/tex] ---> red tone
Find the value of y
[tex]y=1.2z[/tex]---> [tex]y=1.2(5)=6\ oz[/tex] ----> gray tone
