SOLUTION: you have 55 coins totaling $10.00. There are more nickels than pennies, more dimes than nickels and more quarters than dimes. How many of each coin do you have?

Question 211145: you have 55 coins totaling $10.00. There are more nickels than pennies, more dimes than nickels and more quarters than dimes. How many of each coin do you have?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
you have 55 coins totaling $10.00.
There are more nickels than pennies, more dimes than nickels and more quarters than dimes.
How many of each coin do you have?
:
p + n + d + q = 55
:
A lot of unknown here, have to make some assumptions,
has to be a lot of quarters; assume there are 35 quarters
then
p + n + d = 55 - 35
p + n + d = 20
and
.01p + .05n + .10d = 10 - 8.75
.01p + .05n + .10d = 1.25
Multiply by 100
p + 5n + 10d = 125
:
subtract the 1st equation from the above equation:
p + 5n + 10d = 125
p + n + d = 20
------------------------- subtraction eliminates p
0p + 4n + 9d = 105
:
4n = 105 - 9d
n =
Try values for d which give an positive integer value for n that is less than d (only have one)
:
d = 9 then n = 6
find p
p = 20 - 9 - 6
p = 5
:
so we have 5 pennies, 6 nickels, 9 dimes and 35 quarters (55 coins)
:
Check the value:
.01(5) + .05(6) + .10(9) + .25(35) = 10.00
.05 + .30 + .90 + 8.75 = 10

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