x, y, z are the three piles, xr is the number of red cards in x.

8xr + 5zr = 26

This is only true for integers when xr = 4, so xr = 4 and zr = 4. Thus, yr = 18

xr = 4, so xb = 12

yr = 18, so yr = 6

zr = 4, so zb = 8

x = 4+12 = 16

y = 18 + 6 = 24

z = 8 + 4 = 12

Have you taken B1+B2+B3=26 and R1+R2+R3=26 in all your solution sets? I see grom the GIF image that there are many cases where this isn't true (I have not examined all of the solutions yet), which means the solution sets are not acceptable ]]>

here are all the solutions:]]>

B[sub]1[/sub]=3R[sub]1[/sub]

3B[sub]2[/sub]=R[sub]2[/sub]

B[sub]3[/sub]=2R[sub]3[/sub]

Then ... ?

]]>**In the first pile there are three times as many Blacks as Reds.**

**In the second pile there are three times as many Reds as Blacks.**

**In the third pile there are twice as many Blacks as Reds.**

**How many cards of each colour are there in each of the three piles?**