Since Greta's brother received 40 letters, Greta received 40+10 = <<40+10=50>>50 letters.
Together, Greta and her brother received 50 + 40 = <<50+40=90>>90 letters.
Greta's mother received twice the total number of letters Greta and her brother received, which totals 90*2 = <<90*2=180>>180 letters.
In total, the three received 90+180 = <<90+180=270>>270 letters.
#### 270