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.)

Question

Mathematics

Aubrey Fletcher

1 January, 01:43

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.)

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Answers (1)

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Malia Smith · Answer 1

250 cards

Step-by-step 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.