The total ratio of the coins they both have is 10+45 = <<10+45=55>>55
The fraction of the ratio representing the number of coins that Amalie has is 45/55, and since the total number of coins they both have is 440, Amalie has 45/55*440 = <<45/55*440=360>>360 coins.
When Amalie spends 3/4 of what she has, she parts with 3/4*360 = <<3/4*360=270>>270 coins.
She still has 360 coins - 270 coins = <<360-270=90>>90 coins
#### 90