If the number of dimes is 20 times the number of quarters, she has 350/5 = 70 quarters.
When she puts 2/5 of the quarters away, the number of quarters reduces by 2/5*70 = <<2/5*70=28>>28
She's now left with 70-28 = <<70-28=42>>42 quarters.
In total, she has 42 quarters + 350 dimes = <<42+350=392>>392
#### 392