Liam sold 40/2 = <<40/2=20>>20 sets of oranges that cost $2.50 for each set.
So, Liam earned $2.50 x 20 = $<<2.5*20=50>>50.
Claire earned $1.20 x 30 = $<<1.20*30=36>>36.
Thus, they were able to save $50 + $36 = $<<50+36=86>>86 for their mother's birthday gift.
#### 86