One quarter of Steve's baseball cards are from his dad's collection. Another 0.2 are from his uncle, and 0.5 are from his brother. The rest are from Steve's cousin. Thirty of the cards from his cousin are National League players; the other half are American League. How many cards are in his collection?
Uh... I'm guessing that .2 means 20%? Because you can't have .2 of a card? But then the total cards you have sums to over 100% and welp.
total collection ---- x
from dad --- x/4
from uncle --- x/5 ---> (.2)x = (2/10)x = x/5
from brother --- x/2
leaving : x -x/4 - x/5 - x/2 = x/20
so from cousin = x/20
so (1/3)(x/20) = 30
x = 1800
Steve has 1800 cards
check:
from dad = 1800/4 = 450
from uncle = .2(1800) = 360
from brother = (1/2)(1800) = 900
Total of that = 1710
so 1800-1710 or 90 are from cousin
(1/3) of those are NL players
(1/3)(90) = 30 , as it said in the question.
I misread
"Thirty of the cards from his cousin are National League players"
as
one third of the cards from his cousin are NL players
To find out how many cards are in Steve's collection, let's break down the information given step by step:
1. One quarter of Steve's baseball cards are from his dad's collection.
- This means Dad's cards make up 1/4 of Steve's collection.
2. Another 0.2 are from his uncle.
- This means Uncle's cards make up 0.2 of Steve's collection.
3. 0.5 are from his brother.
- This means Brother's cards make up 0.5 of Steve's collection.
4. The rest are from Steve's cousin.
- This means Cousin's cards make up the remaining portion of Steve's collection.
5. Thirty of the cards from his cousin are National League players, and the other half are American League.
- Let's assume the total number of cards in Steve's collection is "X".
- The cards from Cousin are divided into two equal parts, so half of Cousin's cards are American League and half are National League.
- Therefore, 0.5X (0.5 times the total) are National League cards, and 0.5X are American League cards.
Now, let's put all the information together and solve for X, the total number of cards in Steve's collection:
Dad's cards: 1/4X
Uncle's cards: 0.2X
Brother's cards: 0.5X
Cousin's cards: X - (1/4X + 0.2X + 0.5X) = X - (0.95X) = 0.05X
Since we know that 30 cards are from Cousin's collection and are National League players, we can set up the equation: 0.5X = 30.
Solving for X:
0.5X = 30
X = 30 / 0.5
X = 60
So, there are 60 cards in Steve's collection.