Two boxes, A and B, contain some red and blue beads. In Box A, the ratio of the number of red beads to the number of blue beads is 2: 1. In Box B, the ratio of the number of red beads to the number of the blue beads is 1: 3. Box A has thrice as many beads as Box B.

Question

Two boxes, A and B, contain some red and blue beads. In Box A, the ratio of the number of red beads to the number of blue beads is 2: 1. In Box B, the ratio of the number of red beads to the number of the blue beads is 1: 3. Box A has thrice as many beads as Box B.
(a) Find the ratio of the number of red beads in Box A to the number of blue beads in B operatorname Box B.
(b) If 105 red beads are taken out from Box A and placed in Box B, the ratio of the number of red beads to the number of blue beads in Box B becomes 3: 2. What is the total number of beads in the 2 boxes?