I don't know

Let  🔵  = x

Let 🔴 = y

Let ⚪  = z

So....we can write this equation as 

3 [ 100x + 10y  + z]  =  100y + 10y + y

3 [100x + 10y + z ]  = 111y

100x + 10y + z  =  37y

100x + z   = 27y

Then....one possible answer  is if we let  x = 1 and z = 8, then y = 4

100(1) + 8   = 27(4)

108  = 108

So we have that

148  + 148 + 148   =  444

So.....

🔵 = 1

🔴 = 4    and

⚪ = 8

so  🔵=x

🔴=y &

⚪=z

in equation form it is:

(x*y*z)+(x*y*z)+(x*y*z)=y*y*y which we can simplyfy to:

3(x*y*z)=y*y*y which means that

x*y*z=(y³)/3 so

x=(y²) / (3*z)

so we can choose any random numbers for y & z and put them into the formula to work out x. if you want to to work out y it's

y=sqrt(x*3*z)

so we can choose any number for x & z then work out y from that. or for z it's

z=((y²)/x)/3

 i have checked these and they always work. so there is an infinite number of possible solutions. and just out of interest; CPhill says that one answer could be that x=1 y=4 and z=8 but (1*4*8)+(1*4*8)+(1*4*8)=32+32+32=96 but y*y*y=4*4*4=64 so CPhill's answer is saying that 64=96 which is not true. 

148

148