Question

Annie loves giving away puppies. When her friend Bobby walks by, she instantly gives him 50% of her puppy stash. Bobby, stunned with this shower of puppies, gives back 20% of his total. Annie counters by giving Bobby 50% of her new puppy total. Bobby responds by giving Annie back 50% of the puppies he now has and then running off, having gone from 0 to 7 puppies in just a few seconds! How many puppies did Annie begin with?

Answer 1

50% x = x/2 = 0.5x
20% x = 0.2x

Anni start with x, Bobby starts with 0

1)

Annie: x - 50%x = x - 0.5x = 0.5x

Bobby: 0 + 0.5x = 0.5x

2)

Annie: 0.5x + 0.2(0.5x) = 0.5x + 0.1x = 0.6x
Bobby: 0.5x - 0.1x = 0.4x

3)
Annie: 0.6x - 0.5(0.6x) = 0.6x - 0.3x = 0.3x
Booby: 0.4x + 0.3x = 0.7x

4)
Annie: 0.3x + 0.5(0.7x) = 0.3x + 0.35x = 0.65x
Bobby: 0.7x - 0.35x = 0.35x

0.35x = 7

x = 20

Annie began with 20 puppies