The ratio of the number of watermelons shipped to the fruit store to the number of white melons is seven to five. If forty white melons and fifty watermelons are sold every day, the white melons will be sold out after a few days.

Suppose the number of days it takes for the honeydew melons to be sold out is x days.

2(40x)=50x 360,

80x=50x 360,

30x=360,

x=12,

The number of white melons is: 12×40=480 (pieces),

The number of watermelons is: 480×2=960 (pieces),

Watermelons And Bailangua***: 480 960 = 1440 (pieces).

Answer: ***1440 watermelons and honeydew melons were shipped from the fruit shop.

So the answer is: 1440.