Question 8
Initially Bình and Châu have cards in the ratio 2:3. Their mother gives each some cards, and their new totals are still in the ratio 2:3. (For example, mother gives Bình 10 cards and Châu 11 cards.) If the two gifts are exchanged, Bình instead has 12 more cards than Châu. (With the exchange, mother gives Bình 11 cards and Châu 10 cards.) Find the difference between the total number of cards given by mother and the total number the children had initially. Show your reasoning.
Clarification: The parenthetical 10/11 examples illustrate only exchanging the recipients, not the actual gift amounts satisfying the stated ratios.
Clarification: The parenthetical 10/11 examples illustrate only exchanging the recipients, not the actual gift amounts satisfying the stated ratios.