Question

Jack had quite a few hockey cards, and Jill had some of her own. Jack gave Jill as many hockey cards as she already had. Jill then gave Jack back as many cards as he had left. Finally, Jack gave her back as many cards as she had left. This left poor Jack with no cards and left Jill with 40 cards altogether. How many hockey cards did each of them have just before these exchanges took place?

Answer 1

Jack: 25

Jill: 15

Step-by-step explanation:

This is like doing a math problem backwards.

We know there was 40 cards in all, and Jill had all of them in the end.

The third exchange: Jack gave Jill the same amount of cards she already had, which ended up giving Jill all of them. This means they each had half the deck, at 20 cards a piece.

The second exchange: Here, we are trying to get Jack to have 20 cards. Since he received the same amount as he'd already had, and ended up with 20, this means he had to have ten and receive ten. So, Jack had 10 cards, and Jill had 30 cards (which we know because she gave away 10 and ended up with 20 for the next exchange.

The first exchange: Jack gave Jill the same amount of cards as she started with. This means that she had half of 30, which is 15, and Jack gave her 15 more to start the next exchange. Jill started with 15 cards, and Jack started with 25 (which we know because 40 - 15 = 25)

If this was a little hard to follow, read the steps in backwards order from how they are written :) I hope this helps.