# Jason bought 9 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 42 cards left. How many cards did Jason start with?

May 29, 2018

75 cards

#### Explanation:

Let x be the number of cards Jason had initially in his collection.

"Jason bought 9 new baseball trading cards to add to his collection"

$x + 9$ is the equation because $x$ is the initial number of cards he has and he bought another 9

"His dog ate half of his collection"

$\frac{1}{2} \left(x + 9\right)$ because $x + 9$ is what he had before his dog ate his cards and since his dog ate half, there is a $\frac{1}{2}$ added to the equation

"42 cards left"

$\frac{1}{2} \left(x + 9\right) = 42$ Since his dog ate half, he is left with half of his initial card collection.

$x + 9 = 42 \times 2$

$x + 9 = 84$

$x = 84 - 9$

$x = 75$