Question 671512
 Penny has pennies, Nicholas has nickels, Doug has dimes, queen has quarters and
 Harry has half dollars.
Original amts: .01p, .05n, .10d, .25q, .50h
:
Write an equation for each statement:
:
Nicholas has 47 more nickels than Doug has dimes.
n = (d+47)
or
d = (n-47)
:
Penny gives nick 40 pennies.
then their amts are: (.01p-.40) and (.05n+.40)
:
Nick gives Doug 30 nickels. ($1.50)
then their amts are: 
.05n + .40 - 1.50 = (.05n-1.10)
and
(.10d+1.50)
:
Doug gives queen 15 dimes. (1.50)
then their amts are:
.10d+1.50 - 1.50 = (.10d)
and
(.25q+1.50)
:
AT this point we have enough information to find n and d
Since they end up with the same amt, we can write an equation:
.10d = .05n-1.10
replace n with (d-47) from the 1st equation
.10d = .05(d+47) - 1.10
.10d = .05d + 2.35 - 1.10
.10d - .05d = 1.25
.05d = 1.25
d = 1.25/.05
d = 25 dimes, original amt = $2.50 and this is the final amt also
Find n
n = d + 47
n = 25 + 47
n = 72 nickels, original amt .05(72) = $3.60
.
Queen gives Harry 8 quarters. ($2.00)
then their amts are:
.25q + 1.50 - 2.00 = (.25q-.50)
.25q - .50 = 2.50
.25q = 2.50 + .50
.25q = 3.00
q = 3.00/.25
q = 12 quarters, original amt = $2.00
and
.50h + 2.00 
:
Harry gives penny 4 half dollars ($2.00)
then their amts are:
.01p + 2.00 = 2.50
.01p = 2.50 - 200
.01p = .50
p = .50/.01
p = 50 pennies
and
.50h - 2.00 = 2.50
.50n = 2.50 + 2
.50h = 4.50
h = 4.50/.50
h = 9 half dollars or $4.50
:
then each will have the same amount of money. How much did each start with?
p: 50 cents; n: 72*.05 = $3.60; d: 25*.10 = $2.50; q: .25*12 = $3.00; h: 9*.50 = $4.50