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Question

H and M had some cards. H gave 1/4 of her cards to M. Then M gave 1/6 of what she had to H. After that H gave 12 cards to M. In the end H had 40 cards and M has 92 cards. How many cards did H have at first

Answer 1

OK, Kaman, let's work backward.

 

If M gives back the 12 cards to H, then H has 52 and M has 80.

 

M had given 1/6 of her cards to H, so the 5/6 she had left was 80, meaning 1/6 was 80/5= 16 and she had 96 cards before giving H those 16 cards.

 

Before getting those 16 cards, H had 36, which was 3/4 of what she started with. Since 3/4 is 36, 1/4 is 12 and she started with 36 + 12 = 48 cards.

 

Take those 12 cards away from M and she started with 84 cards.

 

Let's check...

 

1/4 of 48 is 12, so H gives M 12 cards and M now has 96. H is left with 36.

 

1/6 of 96 is 16, so M gives H 16 cards and has 80 left. H now has 52.

 

H gives M 12 cards and has 40 left and M has 92.

 

Check!