The Packing of IVIath
Oliver and his friends like to collect and trade cards from a certain combat card game. Oliver used his allowance to purchase 1 booster pack and 3 pre-made decks, which included a total of 143 cards. For his birthday, he received 8 booster packs and 3 pre-made decks, which included a total of 220 cards. How many cards come in every booster pack and every pre-made deck?
If each booster pack has cards and each pre-made deck has cards, then what is ?
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1 solution
To solve using elimination, follow these four steps:
Step 1: Make sure the equations have opposite x terms or opposite y terms.
Step 2: Add to eliminate one variable and solve for the other.
Step 3: Plug the result of Step 2 into one of the original equations and solve.
Step 4: State the solution.
Before you can solve, you must write a system of equations. Let x = the number of cards in a booster pack, and let y = the number of cards in a premade deck.
x + 3y = 143 8x + 3y = 220
Now use elimination to solve the system of equations. -(x + 3y = 143) → -x – 3y = -143 8x + 3y = 220 → 8x + 3y = 220
Add to eliminate the y terms, and then solve for x. Then, Take the result of Step 2, x = 11, and plug it into one of the original equations, such as x + 3y = 143. Then find the value of y. - You should get (11)+3y=143
After words, simplify to get Then subtract 11+3y=143 -11 -11 - To get 3y=132 Divide 3y/3 132/3 Simplify Y=44