my grandfather has a huge coin collection of silver dollars and 50-cent pieces. He promised to give one fourth if his collection to the first of his grandchildren who can figure put the total value of his coins. The only cares he will give are these: There are 133 more silver dollars than 50-cent pieces. The ratio if silver dollars to 50-cent pieces is 5:2. I'm determined to beat my sister and my cousins to the answer! How many of each type of coin is in my grandfather's collection? How much money will I get if I am the first one to answer the question?

Question

my grandfather has a huge coin collection of silver dollars and 50-cent pieces. He promised to give one fourth if his collection to the first of his grandchildren who can figure put the total value of his coins. The only cares he will give are these: There are 133 more silver dollars than 50-cent pieces. The ratio if silver dollars to 50-cent pieces is 5:2. I'm determined to beat my sister and my cousins to the answer! How many of each type of coin is in my grandfather's collection? How much money will I get if I am the first one to answer the question?

Answer 1

If there are d dollars and h halves, then what do we know?

d = h+133
d/h = 5/2

Now you can easily find h and d.

Answer 2

To find the number of each type of coin in your grandfather's collection, we can follow these steps:

Step 1: Assign variables.
Let's assume the number of 50-cent pieces in the collection is x.

Step 2: Set up equations from the given information.
Based on the information given, we know that:
- There are 133 more silver dollars than 50-cent pieces. So the number of silver dollars can be represented as (x + 133).
- The ratio of silver dollars to 50-cent pieces is 5:2. So we can write the equation (x + 133)/x = 5/2.

Step 3: Solve the equation.
Let's cross-multiply our equation to solve for x:
2(x + 133) = 5x

Expanding the equation:
2x + 266 = 5x

Bring the terms with x to one side:
5x - 2x = 266

3x = 266

Divide both sides by 3:
x = 88.7

Since you cannot have a fraction of a coin, we round x to the nearest whole number:
x ≈ 89

So, there are approximately 89 50-cent pieces in your grandfather's collection.

Step 4: Calculate the number of silver dollars.
Using the equation x + 133, substitute the value of x:
89 + 133 = 222

So, there are 222 silver dollars in your grandfather's collection.

Step 5: Calculate the total value of the coins.
Silver dollars and 50-cent pieces have face values of $1 and $0.50, respectively.
To find the total value, multiply the number of coins by their face values and add them together:

Total value = (Number of silver dollars x $1) + (Number of 50-cent pieces x $0.50)
Total value = (222 x $1) + (89 x $0.50)
Total value = $222 + $44.50
Total value = $266.50

So, if you are the first one to answer the question correctly, you will receive one-fourth of the total value:
Your share = (1/4) x $266.50
Your share ≈ $66.63

Therefore, if you are the first one to answer, you will receive approximately $66.63 from your grandfather's coin collection.