How many cards did Benny start with?

Question

Benny bought 6 new baseball cards to add to his collection. The next day his dog ate half of his collection. They are now only 42 cards left. How many cards did Benny start with?

Answer 1

Let N be the number of cards with which Benny started. He added 6 to his collection, so then he had N + 6. But, then his dog at half of his cards leaving him with (N + 6)/2. But, we are told that half of his cards equals 42. Thus, we solve the following equation for N:

 

(N + 6)/2 = 42

 

Multiply both sides by 2. And we get

 

N + 6 = 84.

 

Now, we can subtract 6 from both sides of the equation. This yields:

 

N = 78

Answer 2

c = cards at begining

 

c + 6 - (c + 6)/2 = 42   Multiply everything by 2

2c + 12 - (c + 6) = 84

2c + 12 - c - 6 = 84

c + 6 = 84

c = 78

 

Benny started with 78 cards.