SOLUTION: liviana has $ 2.20 in coins in her change purse. if there is a total of 15 coins how many quarters,dimes,nickles,and pennies does she have?

Question 648794: liviana has $ 2.20 in coins in her change purse. if there is a total of 15 coins how many quarters,dimes,nickles,and pennies does she have?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
There are 4 unknowns but only 2 possible
equations, so this can't be solved directly,
but it still can be figured out.
Let = number of pennies
Let = number of nickels
Let = number of dimes
Let = number of quarters
The equations are:
(1)
(2) ( in cents )
------------------------------------------
The logic steps are:
(a)
There doesn't have to be any pennies,
although there might be, but they will be in
multiples of 5 or 10
(b)
I know there must be less than 9 quarters, since
9 x 25 = 225, which is too much
(c)
I know there must be more than 2 quarters since
2 x 25 = 50, that leaves 13 coins to make $1.70
and even if I have 13 dimes, that is only $1.30
(d)
Likewise, there must be more that 3 quarters
3 x 25 = 75 and 220 - 75 = 145, and
12 x10 = 120 which doesn't make it
(e)
Also, there must be more than 4 quarters
4 x 25 = 100 and 220 - 100 = 120
There are 11 coins left to make $1.20
and 11 x 10 = 110, too small
(f)
It is possible with 5 quarters since
5 x 25 = 125 and 220 - 125 = 95
and 10 x 10 = 100, so it's possible
--------------------------------
5q = 125 which is 5 coins leaving 10
220 - 125 = 95
9d = 90 leaving 1 coin
1 x 5 = 5
So, the answer is
5q
9d
1n
But if I have to use pennies it doesn't work
--------------------------
I'll try
6q
5d
4n
This works, but still no pennies
---------------------------
I'll try
7q
1d
This leaves 7 coins to make 35 cents
and no room for pennies
---------------------
8q
1d
Leaves 6 coins to make 10 cents
that's
1n
5p
That's it
------------
8 quarters, 1 dime, 1 nickel, and 5 pennies
are 15 coins that make $2.20

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