Sum of the ratio 5 : 1 = 6

Let the number of Stamps be = x

Number of stamps Richard has = 5 / 6 of x

Number of stamps Vanessa has = 1/6 of x

Richard gives 45 stamps to Vanessa, So Richard has (5/6)x - 45

Sum of the new ratio 1 : 2 = 3

Number of stamps Richard has now : 1/3 of x = (5/6)x - 45

x/3 = 5x/6 - 45

x/3 - 5x/6 = -45

(2x - 5x)/6 = -45

-3x = - 45 × 6

x = 90

Therefore, Number of stamps = 90

Richard had 75, Vanessa had 15.

After Richard gave 45 stamps , Richard has 30, Vanessa has 60.