Please help me solve this problem. My grandfather has a big collection of silver dollars and 50 cents pieces. He promised to give one fourth of his collection to the first of his grandchildren, who can figure out the total value of his coins. The only clues he will give are these:
There are 132 more silver dollars than 50-cents pieces
The ratio of the silver dollars to 50-cent pieces is 5:2.
I am determined to beat my sister and my cousins to the answer: How many of each type of coins is in my grandfather collection?--------------
How much money will I get if am the first one to answer the question?------
just put the clues into symbols. if there are d dollars and h halves,
d = h+132
d/h = 5/2
clearing the fractions, we have
2d = 5h
now substitute in for d and we have
2(h+132) = 5h
3h = 264
h = 88
so, d = 88+132 = 220
the reward is 1/4 (88/2 + 220) = 1/4 (44+220) = 11+55 = $66
To solve this problem, we can use algebraic equations. Let's assign variables to unknown quantities:
Let x represent the number of 50-cent pieces.
Since there are 132 more silver dollars than 50-cent pieces, the number of silver dollars can be represented as (x + 132).
The ratio of silver dollars to 50-cent pieces is 5:2, so we can set up the equation:
(x + 132) / x = 5 / 2
To solve for x, we can cross-multiply:
2(x + 132) = 5x
Expanding and simplifying:
2x + 264 = 5x
264 = 5x - 2x
264 = 3x
x = 88
So, there are 88 50-cent pieces in your grandfather's collection.
To find the number of silver dollars, we substitute the value of x into the equation:
x + 132 = 88 + 132 = 220
Therefore, the number of silver dollars is 220.
So, your grandfather's collection consists of 88 50-cent pieces and 220 silver dollars.
Now, to determine how much money you will get if you are the first one to answer the question, we need to know the value of each coin.
The value of a 50-cent piece is $0.50 (as the name implies).
The value of a silver dollar is $1.00.
So, if you are the first one to answer the question, you would receive one-fourth of the total value of the collection.
To find the total value, we multiply the number of 50-cent pieces by $0.50 and the number of silver dollars by $1.00:
Value of 50-cent pieces = 88 x $0.50 = $44.00
Value of silver dollars = 220 x $1.00 = $220.00
Total value of the collection = $44.00 + $220.00 = $264.00
If you are the first one to answer the question, you would receive one-fourth of $264.00:
$264.00 / 4 = $66.00
So, if you are the first to answer, you would receive $66.00 from your grandfather's collection.