Mr. Hundley has a big collection of silver dollars and 50-cent pieces. He promised to give one fourth of his collection to the first teacher who can figure out the total values of his coins. These are the only clues:
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 coins is in Mr. Hundley's collection? How much money will I get if I'm the first?
Let there be d dollars, and h halves.
d = h+132
d/h = 5/2
d = 5h/2
5h/2 = h + 132
3h/2 = 132
h = 44
d = 44+132 = 176
Assuming 1/4 of the collection means 1/4 of each kind of coin, then you will get 11 halves and 44 dollars = $49.50
Rats. h=88 (2/3 of 132, not 1/3)
d = 220
1/4 of collection = 44 halves and 55 dollars = $77.00
RATS! I gotta start doing these on paper first.
1/4 collection = 22 halves and 55 dollars = $66
That's my final answer!
There are 132 more silver dollars than 50-cent pieces or D = H + 132.
The ratio of silver dollars to 50-cent pieces is 5:2 or D/H = 5/2.
How many of each type of coins are in Mr. Hundley's collection?
D = 5H/2
Therefore,
5H/2 = H + 132
5H = 2H + 264
3H = 264
H = 88
D = 88 + 132 = 220
88(.50) + 220(1.00) = $264
Your share is (1/4)x264 = $66
You need to finish reading a 300-page book for English class. You have read 135 pages and have only 6 days left to finish the book. How many pages would you need to read each day?
To find out how many of each type of coins Mr. Hundley has, and consequently how much money you will get if you are the first to figure out the total values, let's use algebra to solve the problem step by step.
Let's assume the number of 50-cent pieces is x. This means that the number of silver dollars is x + 132 (as there are 132 more silver dollars than 50-cent pieces).
Given that the ratio of silver dollars to 50-cent pieces is 5:2, we can set up the equation:
(x + 132)/x = 5/2
To simplify this equation, we can cross-multiply:
2(x + 132) = 5x
Expand and simplify:
2x + 264 = 5x
Subtract 2x from both sides:
264 = 3x
Divide both sides by 3:
x = 88
So, Mr. Hundley has 88 50-cent pieces.
To find the number of silver dollars, we can substitute the value of x back into the equation:
x + 132 = 88 + 132 = 220
Therefore, Mr. Hundley has 220 silver dollars.
To calculate the total value of the coins, we need to know the face value of each coin. Let's assume the face value of a silver dollar is $1 and the face value of a 50-cent piece is $0.50.
The value of the silver dollars is 220 * $1 = $220.
The value of the 50-cent pieces is 88 * $0.50 = $44.
So, the total value of the coins is $220 + $44 = $264.
Since Mr. Hundley promised to give one fourth of his collection to the first teacher who figures out the total values, you would receive one fourth of the total value:
1/4 * $264 = $66.
Therefore, if you are the first to figure out the total values, you would receive $66.