David and Sam had some games cards at a ratio of 4:5. Both later collected some more cards. As a result, David collected another 50% of his original number of cards and Sam collected 2 times his original number of cards. If Sam had 40 more game cards than David, how many cards did they have altogether in the end?

cards

After they collected some more cards, the ratio would come to a new form

The ratio of game cards of David and Sam changed to 6:10; we’ve known the difference that is Sam had 40 more game cards than David.

Then, we can make a proportion:

By cross–product,

Sum = 16 × 40 ÷ 4 = 160

Thus, they had 160 games cards in the end.