Question 833820: Hello, I am not understanding what I need to do. It has been a while since I was in school and I have decided to go back but I am stuck on this problem. Could you help me? Please and Thank you!
Question:
There is a pile of nickels and pennies on the table. The total value of the coins is less than two dollars. Also, if the pennies were turned into dimes, and the nickels turned into pennies the value of the coins would be the same. How many coins are in the pile?
Work so far:
x = nickels ---> turned into pennies
y = pennies ---> turned into dimes
Total value is less than $2.00
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
I like to use letters that remind me of what they stand for.
So I use:
n = the number of nickels
p = the number of pennies
$0.05n = the monetary value of the n nickels
$0.01p = the monetary value of the p pennies
Total value = $0.05n + $0.01p
If the p pennies were turned into dimes, their monetary value would be $0.10p.
If the n nickels were turned into pennies, their monetary value would be $0.01n.
Total value would be = $0.10p + $0.01n.
We set those values equal:
$0.05n + $0.01p = $0.10p + $0.01n
Solve for p in terms of n
Drop the dollar marks and multiply every term by 100
to remove the decimals:
5n + p = 10p + n
4n = 9p
 = p
So n must be divisible by 9 in order to divide
evenly into 4n
Then the value is
0 ≦ $0.05n + $0.01p < 2.00
0 ≦ 5n + p < 200
0 ≦ 5n + 4n/9 < 200
0 ≦ 45n + 4n < 1800
0 ≦ 49n < 1800
0 ≦ n < 36.73469388
0 ≦ n < 36
So n can equal 0, 9, 18, 27, 36
And since = p
So p can equal  ,  ,  ,  , 
That is, p can equal 0, 4, 8, 12, 16
So the 5 solutions are:
1. We can have 0 nickels and 0 pennies, and 0 coins. Total = $0.00
If the 0 pennies were turned into 0 dimes, their monetary value
would be 0·$0.10 = $0.00. And,
if the 0 nickels were turned into 0 pennies, their monetary value
would be 0·$0.01. And the total would be $0.00.
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2. We can have 9 nickels and 4 pennies, and 13 coins. Total = $0.49
If the 4 pennies were turned into 4 dimes, their monetary value
would be 4·$.10 = $0.40. And,
if the 9 nickels were turned into 9 pennies, their monetary value
would be 9·$0.01 = $0.09. And the total would be $0.49.
-----------------------------------------------------------
3. We can have 18 nickels and 8 pennies, and 26 coins. Total = $0.98
If the 8 pennies were turned into 8 dimes, their monetary value
would be 8·$.10 = $0.80. And,
if the 18 nickels were turned into 18 pennies, their monetary value
would be 18·$0.01 = $0.18. And the total would be $0.98.
-----------------------------------------------------------
4. We can have 27 nickels and 12 pennies, and 39 coins. Total = $1.47
If the 12 pennies were turned into 12 dimes, their monetary value
would be 12·$.10 = $1.20. And,
if the 27 nickels were turned into 27 pennies, their monetary value
would be 27·$0.01 = $0.27. And the total would be $1.47.
-----------------------------------------------------------
5. We can have 36 nickels and 16 pennies, and 52 coins. Total = $1.96
If the 16 pennies were turned into 16 dimes, their monetary value
would be 16·$.10 = $1.60. And,
if the 36 nickels were turned into 36 pennies, their monetary value
would be 36·$0.01 = $0.36. And the total would be $1.96.
-----------------------------------------------------------
Edwin
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