Question

Seth sold 20% of his baseball cards during week one. During week two, he bought 20% more cards than he had after week one. If he now has 10 fewer cards, how many cards did he have originally? (he had more than 100 cards originally.)

Answer 1

250 cards

Explanation:

Let the number of baseball cards he originally had be x.

He sold 20% of the baseball cards after week one. This means that after week one the number of cards he had was:

x - (20/100 * x) = x - 0.2x = 0.8x

During week two he bought 20% more cards than he had after week one. This means that after week two, he had:

0.8x + (20/100 * 0.8x)

= 0.8x + (0.2 * 0.8x)

= 0.8x + 0.16x = 0.96x

He now has 10 fewer cards. This means that:

x - 10 = 0.96x

Collecting like terms:

x - 0.96x = 10

0.04x = 10

=> x = 10/0.04 = 250

He had 250 cards originally.