Question 671512: Penny has pennies, Nicholas has nickels, Doug has dimes, queen has quarters and Harry has half dollars. Nicholas has 47 more nickels than Doug has dimes.
Penny gives nick 40 pennies.
Nick gives Doug 30 nickels.
Doug gives queen 15 dimes.
Queen gives Harry 8 quarters.
Harry gives penny 4 half dollars then each will have the same amount of money. How much did each start with?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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
|
|
|
