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:

Question

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?------

Steve · Answer

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