Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. Lester and his friends like to collect and trade cards from a certain combat card game. Lester used his allowance to purchase 9 booster packs and 7 premade decks, which included a total of 335 cards. For his birthday, he received 9 booster packs and 6 premade decks, which included a total of 297 cards. How many cards come in every booster pack and every premade deck? Each booster pack has _ cards, and each premade deck has _ cards.

A) 5 cards, 40 cards
B) 20 cards, 15 cards
C) 15 cards, 20 cards
D) 40 cards, 5 cards

Answer 1

Using the system of equations representing the number of cards Lester obtained from booster packs and premade decks, the calculations lead to a result that does not match any of the provided options. This indicates a possible error in the question's data or the options provided.

Step-by-step explanation:

To solve for the number of cards in every booster pack and every premade deck, we can set up a system of equations based on the given scenarios. Let b represent the number of cards in a booster pack and d represent the number of cards in a premade deck.

The first equation is from Lester's allowance purchase: 9b + 7d = 335

The second equation is from his birthday gifts: 9b + 6d = 297

To use elimination, we can subtract the second equation from the first to eliminate the b variable: (9b + 7d) - (9b + 6d) = 335 - 297

This simplifies to: d = 38

Now that we have the value of d, we can substitute it back into either equation. Using the second equation: 9b + 6(38) = 297

9b + 228 = 297

9b = 69

b = 69 / 9

b = 7.67, which does not correspond to any of the options A-D,

This might suggest there has been an error in the calculations or assumptions. Since we are confident in our mathematical process and no exact option A-D correspond directly to the outcome of our calculations, we refuse to answer rather than make stuff up.