Question

My grandfather has a big collection of silver dollars and 50-cent pieces. He promised to give 1/4 of his collection to the first of grandchildren who can figure out the value of his coins. The only clues he will give are these:

There are 132 more silver dollars than 50-cent pieces.
The ratio of silver dollars to 50-cent pieces is 5:2

How many of each type of coin is in my grandfather's collection? How much money do I get if I'm the first one to answer the questiion?

Answer 1

Let's start by setting up some equations based on the information given in the problem.

Let x be the number of 50-cent pieces in the collection.

Then the number of silver dollars in the collection is x + 132 (since there are 132 more silver dollars than 50-cent pieces).

The ratio of silver dollars to 50-cent pieces is given as 5:2, which means that:

(x + 132) / x = 5/2

We can cross-multiply to solve for x:

2(x + 132) = 5x

2x + 264 = 5x

264 = 3x

x = 88

So there are 88 50-cent pieces in the collection, and 88 + 132 = 220 silver dollars.

To calculate the value of the coins, we need to know the face value of each coin. A silver dollar has a face value of $1, and a 50-cent piece has a face value of $0.50. Therefore, the total value of the coins is:

220($1) + 88($0.50) = $220 + $44 = $264

If you are the first grandchild to figure this out, you would receive 1/4 of the total value of the coins, which is:

(1/4)($264) = $66