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#1:
2005 Chapter Team-- A standard deck of playing cards with 26 red cards
and 26 black cards is split into two piles, each having at least one
card. In pile A there are six times as many black cards as red cards. In
pile B, the number of red cards is a multiple of the number of black
cards. How many red cards are in pile B?**Problems: (Solutions below)**#2: 2000 State sprint #30. Joe bought a pumpkin that cost cents more per pound than his sister's. Together, the two pumpkins weighed pounds, but Joe's pumpkin was heavier. Joe paid dollars and his sister paid cents. How many pounds did Joe's pumpkin weigh?

Solutions :

#1: You know the total cards in pile A is a multiple of 7 because there are six times as many black cards as the red cards. (given)

6 Black, 1 Red on pile A gives you 20 Black and 25 Red cards on pile B. (doesn't work)

12 Black and 2 Red cards on pile A gives you 14 Black and 24 Red cards on pile B. (doesn't work)

18 Black and 3 Red cards on pile A gives you 8 Black and 23 Red cards on pile B. (doesn't work)

24 Black and 4 Red cards on pile A gives you 2 Black and 22 Red cards on pile B. Yes!!

The answer is**22**Red cards.

#2:

**Solution I :**

**Solution II: Make a list:**

Joe's sister Joe

1 lb. 19 lb. (doesn't work since 19 x 58 cents are too much)

2 lbs. 18 lbs (doesn't work)

3 lbs. 17 lbs (No)17 x (48/3 + 10) = 442 (still too much)

4 lbs 16 lbs 16 x (48/4 + 10)= 352 (yes)

The answer is **16**pounds.