Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks. Pedro and his friends like to collect and trade cards from a c... Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks. Pedro and his friends like to collect and trade cards from a certain combat card game. Pedro used his allowance to purchase 9 booster packs and 6 premade decks, which included a total of 360 cards. For his birthday, he received 1 premade deck, which included a total of 48 cards. How many cards come in every booster pack and every premade deck? Each booster pack has _____ cards, and each premade deck has _____ cards. Read more

Steps to Solve

1. Define Variables

Let:

• ( x ) = number of cards in each booster pack
• ( y ) = number of cards in each premade deck

2. Set Up the First Equation

From the information given about the 9 booster packs and 6 premade decks totaling 360 cards: $$ 9x + 6y = 360 $$

3. Set Up the Second Equation

From the birthday gift of 1 premade deck with 48 cards: $$ y = 48 $$

4. Substitute the Second Equation into the First

Substituting ( y = 48 ) into the first equation: $$ 9x + 6(48) = 360 $$

5. Solve for (x)

Calculate: $$ 9x + 288 = 360 $$

Now subtract 288 from both sides: $$ 9x = 360 - 288 $$ $$ 9x = 72 $$

Now divide both sides by 9 to find (x): $$ x = \frac{72}{9} $$ $$ x = 8 $$

6. State the Values of ( x ) and ( y )

We have found:

• ( x = 8 ) (cards in each booster pack)
• ( y = 48 ) (cards in each premade deck)