If the blue lantern is X, the yellow lantern is (1+2/5)x, and the red lantern is (1-4/7) (1+2/5) X.

x+( 1+2/5)x+[( 1-4/7)( 1+2/5)]x = 450

x+7/5x+[3/7x7/5]x=450

x+7/5x+3/5x=450

( 1+7/5+3/5)x=450

3x=450

x = 450 \3

x= 150

150x (1+2/5) = 210 (pieces)

2 10x( 1-4/7)=90 (piece)

A: There are 90 red lanterns, 2 yellow lanterns10 and blue lanterns 150.