Question

"Finn used his allowance to purchase 7 booster packs and 4 premade decks, totaling 265 cards. For his birthday, he received 4 booster packs and 1 premade deck, totaling 91 cards. To find out how many cards come in every booster pack and every premade deck, we can set up the following equations:

7x (number of cards in each booster pack) + 4y (number of cards in each premade deck) = 265
4x (number of cards in each booster pack) + y (number of cards in each premade deck) = 91

Solving this system of equations will give us the values of x and y, representing the number of cards in each booster pack and each premade deck, respectively."

Answer 1

To find the number of cards in each booster pack and premade deck, we need to solve the system of equations. The number of cards in each booster pack is 11, and the number of cards in each premade deck is 47.

Step-by-step explanation:

To find the number of cards in each booster pack and premade deck, we need to solve the system of equations given. Let's assign variables:

Let x be the number of cards in each booster pack.

Let y be the number of cards in each premade deck.

The first equation is 7x + 4y = 265, and the second equation is 4x + y = 91.

We can solve these equations simultaneously using substitution or elimination method.

If we use substitution, we can solve the second equation for y in terms of x: y = 91 - 4x.

Substituting this into the first equation, we get 7x + 4(91 - 4x) = 265.

Simplifying this equation, we have 7x + 364 - 16x = 265.

Combining like terms, we get -9x = -99.

Dividing both sides by -9, we find that x = 11.

Substituting this value of x into the second equation, we have 4(11) + y = 91.

Simplifying this equation, we get 44 + y = 91.

Subtracting 44 from both sides, we find that y = 47.

Therefore, there are 11 cards in each booster pack and 47 cards in each premade deck.