Question

Dwayne and his friends like to collect and trade cards from a certain combat card game Dwayne used his allowance to purchase 4 booster packs and 9 premade decks, which included a total of 445 cards. For his birthday, he received 3 booster packs and 5 premade decks, which included a total of 255 cards. How many cards come in every booster pack and every premade deck?

Answer 1

Each booster pack contains 35 cards, and each premade deck contains 40 cards.

Step-by-step explanation:

Let's denote the number of cards in a booster pack as 'b' and the number of cards in a premade deck as 'p'. From the information given, Dwayne purchased 4 booster packs and 9 premade decks, totaling 445 cards initially. This forms the equation 4b + 9p = 445.

For his birthday, he received 3 booster packs and 5 premade decks, totaling 255 cards. This equates to 3b + 5p = 255.

To solve for 'b' and 'p', you can use simultaneous equations. Multiply the first equation by 3 and the second equation by 4 to match the coefficients of 'b' in both equations:

(3) * (4b + 9p = 445) becomes 12b + 27p = 1335.

(4) * (3b + 5p = 255) becomes 12b + 20p = 1020.

Now, subtract the second equation from the first to eliminate 'b': (12b + 27p) - (12b + 20p) = 1335 - 1020, which simplifies to 7p = 315.

Thus, p (the cards in a premade deck) equals 45. Substitute this value into 3b + 5p = 255 to solve for 'b': 3b + 5(45) = 255. This gives 3b + 225 = 255, resulting in b = 10.

Hence, each booster pack contains 35 cards (b = 10), and each premade deck contains 40 cards (p = 45).