Jane and Fred each have their own collection of red and blue bingo chips. The ratio of the number of Jane’s chips to the number of Fred’s chips is 3:2. When they combine their chips, the ratio of the number of red chips to the number of blue chips is 7:3. For Jane’s chips, the ratio of the number of red chips to the number of blue chips is 4:1.

What is the ratio of the number of red chips to the number of blue chips for Fred’s bingo chips?

#Jane's chips= 3x, #Fred's chips = 2x

# Red Chips = 7y, # Blue chips = 3y

# Jane's Red Chips = 4z, # Jane's Blue chips = z

Total # chips = 5x = 10y

=> x= 2y

Therefore, #Jane's chips = 6y, # Fred's chips = 4y

#Jane's chips = 5z= 6y

=> z = 6k, y = 5k

Accordingly,

#Fred's Blue chips = Total # Blue chips - Jane's Blue chips = 3y - z = 3*5k - 6k = 9k

#Fred's Red chips = Total # Red chips - Jane's Red Chips = 7y- 4z = 7*5k - 4*6k = 35k - 24k = 11k

Consequently, the required ratio = 11k:9k == 11:9