Question 460447: a piggy bank contains nickels, dimes, and quarters. The number of dimes is three more than the number of nickels and the number of quarters is four less than the number of nickels. If the value of the coins is less than $10, what is the maximum number of nickels in the bank?
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
>>...The number of dimes is three more than the number of nickels...<<
d = n + 3
>>...the number of quarters is four less than the number of nickels...<<
q = n - 4
>>...the value of the coins is less than $10,...<<
$0.05n + $0.10d + $0.25q < $10.00
Multiply that by 100 and drop $ marka:
5n + 10d + 25q < 1000
Divide through by 5
n + 2d + 5q < 200
Substitute d = n + 3 and q = n - 4
n + 2(n + 3) + 5(n - 4) < 200
n + 2n + 6 + 5n - 20 < 200
8n - 14 < 200
8n < 214
n < 26.75
The answer is 26 nickels. for that is the largest whole number
that does not exceed 26.75
In fact the maximum number of dimes, the maximum number of
nickels, and the maximum number of quarters are all three
achieved if the piggy bank contains $9.70 with 29 dimes,
26 nickels and 22 quarters.
Edwin
|
|
|
