<PRE><B>Question 952187</B>
p = no.of pennies
n = no. of nickles
d = no. of dimes
q = no. of quarters
:
write an equation for each statement
:
 My piggy bank contains 29 coins, each of which is either a penny, nickel, dime, or quarter.
p + n + d + q = 29
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The total value of all the coins is $2.86,
.01p + .05n + .10d + .25q = 2.86 
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 and the number of quarters is equal to the sum of the nickels and dimes, 
q = n + d
d = q - n
n = q - d 
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and is less than the number of pennies.
q &lt; p
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In the 1st equation replace n + d with q and you have
p + 2q = 29
p = -2q + 29
From the above equation and the total$ equation we know the number of pennies has to be 21 or 11 pennies which would make it 4 or 9 quarters
.01p + .05n + .10d + .25q = 2.86
lets say 9 quarters and 11 pennies
.11 + .05n + .10d + .25(9) = 2.86
.11 + .05n + .10d + 2.25 = 2.86
.05n + .10d + 2.36 = 2.86
.05n + .10d = 2.86 - 2.36
.05n + .10d = .50
simplify, divide by .05
n + 2d = 10
we know the d = q - n, d = 4 - n
n + 2(9-n) = 10
n + 18 - 2n = 10
-n = 10 - 18
-n = -8
n = 8 nickels
:
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Check this find the dimes
8 + 2d = 10
2d = 2
d = 1 dime
:
11 + 8 + 1 + 9 = 29
and
.01(11) + .05(8) + .10(1) + .25(9) = 2.86
.11 + .40 + .10 + 2.25 = 2.86

--------------------Response to Comment-----------------------
Tried sending this to the given email address, came back as &quot;Milbox not available&quot;
:
Yes, well to start with, we have 4 unknowns and only 3 meaningful equations, which means we will have to apply some logical assumptions
Assuming you followed me Ok up to the equation: 
p = –2q + 29
Since we have a total of 2.86, and the total of the rest of the coins have to be a multiple of 5, the number of pennies have to end in a 1 or a 6
and looking at the above equation, subtract 2q from 29 will give you an odd number of pennies less than 29 of course, leaves us with a choice of 11 or 21 pennies
This narrows it down to a manageable, try it and see” situation
We can find the number of quarters with either p=11 or p=21
-2q + 29 = 11
-2q = 11 – 29
-2q = –18
q = –18/-2
q = 9 quarters
 
The other alternative, when p = 21
-2q + 29 = 21
-2q = 21 – 29
q = –8/-2
q = 4 quarters
 
Hence the statement,
”From the above equation and the total$ equation we know the number of pennies has to be 21 or 11 pennies which would make it 4 or 9 quarters”
:
Hopefully it made made sense to you after that. If not, email me your concerns about this,  email me at ankor@att.net
 

 






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