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?
30 + 30 = 60 cards from cousin
X - 1/4X - .2X - .5X = 60
Solve for X.
Let's solve this step by step:
1. We know that one quarter (0.25) of Steve's baseball cards are from his dad's collection.
2. We also know that another 0.2 (20%) of the cards are from his uncle.
3. Additionally, 0.5 (50%) of the cards are from his brother.
4. The remaining cards are from Steve's cousin.
5. We are given that 30 of the cards from his cousin are National League players, and the other half are American League players.
Let's calculate the number of cards step by step:
Step 1: Calculate the number of cards from his dad's collection:
Let C be the total number of cards in Steve's collection.
The number of cards from his dad's collection is 0.25 * C.
Step 2: Calculate the number of cards from his uncle's collection:
The number of cards from his uncle's collection is 0.2 * C.
Step 3: Calculate the number of cards from his brother's collection:
The number of cards from his brother's collection is 0.5 * C.
Step 4: Calculate the number of cards from his cousin's collection:
The number of cards from his cousin's collection can be calculated by subtracting the cards from his dad, uncle, and brother's collection from the total number of cards.
Number of cards from cousin = C - (0.25 * C + 0.2 * C + 0.5 * C).
Step 5: Calculate the number of National League cards from his cousin's collection:
We are given that 30 cards from his cousin are National League players.
So, the number of National League cards from his cousin is 30.
Step 6: Calculate the number of American League cards from his cousin's collection:
Since the other half of the cousin's cards are American League players, the number of American League cards is also 30.
Now, we can set up an equation to solve for the total number of cards:
Total number of cards = Cards from dad + Cards from uncle + Cards from brother + Cards from cousin
C = 0.25C + 0.2C + 0.5C + (C - (0.25C + 0.2C + 0.5C))
Let's solve this equation:
C = 0.25C + 0.2C + 0.5C + (C - (0.25C + 0.2C + 0.5C))
C = 0.25C + 0.2C + 0.5C + C - 0.25C - 0.2C - 0.5C
C = 1.5C - 0.95C
0.5C = 1.5C - 0.95C
0.5C = 0.55C
Simplifying further, we find:
C = 0.5C / 0.55
C ≈ 0.9091C
Now, we can solve for C:
C = 0.9091C
1 = 0.9091
So, the total number of cards in Steve's collection is 1. We can interpret this as 100% of the cards in his collection.
Therefore, Steve's collection has 1 card.
To find the total number of cards in Steve's collection, let's break down the information given step by step.
1. One quarter (0.25) of Steve's cards are from his dad's collection.
2. Another 0.2 of Steve's cards are from his uncle.
3. 0.5 of Steve's cards are from his brother.
4. The remaining cards are from his cousin.
5. 30 of the cards from his cousin are National League players, and the other half are American League players.
Let's calculate the number of cards we know about:
1. Dad's cards: 0.25 * Total number of cards
2. Uncle's cards: 0.2 * Total number of cards
3. Brother's cards: 0.5 * Total number of cards
4. Cousin's cards: (Total number of cards - (Dad's cards + Uncle's cards + Brother's cards))
Now, let's set up an equation to solve for the total number of cards in Steve's collection:
Total number of cards = Dad's cards + Uncle's cards + Brother's cards + Cousin's cards
We know:
Dad's cards = 0.25 * Total number of cards
Uncle's cards = 0.2 * Total number of cards
Brother's cards = 0.5 * Total number of cards
Now, let's plug these values into the equation:
Total number of cards = (0.25 * Total number of cards) + (0.2 * Total number of cards) + (0.5 * Total number of cards) + (Total number of cards - (0.25 * Total number of cards) - (0.2 * Total number of cards) - (0.5 * Total number of cards))
Simplify the equation:
Total number of cards = 0.25 * Total number of cards + 0.2 * Total number of cards + 0.5 * Total number of cards + Total number of cards - 0.25 * Total number of cards - 0.2 * Total number of cards - 0.5 * Total number of cards
Now, we can combine like terms:
Total number of cards = (0.25 + 0.2 + 0.5 + 1 - 0.25 - 0.2 - 0.5) * Total number of cards
Total number of cards = (1 - 0.25 - 0.2 - 0.5) * Total number of cards
Total number of cards = (1 - 0.95) * Total number of cards
Total number of cards = 0.05 * Total number of cards
To eliminate the variable, we can divide both sides of the equation by 0.05:
Total number of cards / 0.05 = (0.05 * Total number of cards) / 0.05
Total number of cards / 0.05 = Total number of cards
Therefore, any value for the total number of cards divided by 0.05 will give the total number of cards in Steve's collection.
In conclusion, the given information does not provide a specific number of cards in Steve's collection. It only provides proportions and fractions of cards from different sources.