Question 363977: Priscilla has pennies, Nate has nickels, Dem has dimes, Qasi has quarters, and Hawthorne has half dollars. Nate has five times as many nickels as Dem has dimes. If Priscilla gives 35 pennies to Nate, 80 pennies to Dem, 50 pennies to Qasi, 10 pennies to Hawthorne, and Nathaniel gives 45 nickels to Dem, 5 nickels to Qasi, 2 nickels to Hawthorne, 1 nickel to Priscilla, and Dem gives 10 dimes to Qasi, 3 dimes to Hawthorne, 2 dimes to Priscilla, 3 dimes to Nate, and Qasi gives 2 quarters to Hawthorne, 9 quarters to Priscilla, 2 quarters to Nate, 3 quarters to Dem, and Hawthorne gives 4 half dollars to Priscilla, 3 half dollars to Nate, 2 half dolars to Dem, and 1 half dollar to Qasi, they will all have the same amount of money. How many coins did each start the problem with?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Priscilla has pennies, Nate has nickels, Dem has dimes, Qasi has quarters, and Hawthorne has half dollars.
:
Nate has five times as many nickels as Dem has dimes.
n = 5d
:
If Priscilla gives 35 pennies to Nate, 80 pennies to Dem, 50 pennies to Qasi, 10 pennies to Hawthorne,
.01p-(35+80+50+10); subtract from Priscilla's pennies
.01p-1.75
Add to the others
.05n + .35
.10d + .80
.25q + .50
.50h + .10
:
:
Nathaniel gives 45 nickels to Dem, 5 nickels to Qasi, 2 nickels to Hawthorne, 1 nickel to Priscilla,
(.05n+.35)-(2.25+.25+.10+.05)
.05n +.35 - 2.65
.05n - 2.30
:
.10d + .80 + 2.25
.10d + 3.05
:
.25q + .50 + .25
.25q + .75
:
.50h + .10 + .10
.50h + .20
:
p-1.75 + .05
p-1.70
:
Dem gives 10 dimes to Qasi, 3 dimes to Hawthorne, 2 dimes to Priscilla, 3 dimes to Nate,
.10d + 3.05 -(1.00+.30+.20+30)
.10d + 3.05 - 1.80
.10d + 1.25
:
.25q+.50+1.00
.25q + 1.50
:
.50h + .20 + .30
.50h + .50
:
p - 1.70 + .20
p - 1.50
:
.05n - 2.30 + .30
.05n - 2.00
:
:
Qasi gives 2 quarters to Hawthorne, 9 quarters to Priscilla, 2 quarters to Nate, 3 quarters to Dem,
.25q + 1.50 -(.50+2.25+.50+.75)
.25q + 1.50 - 4.00
.25q - 2.50
:
.50h + .50 + .50
.50h + 1.00
:
p - 1.50 + 2.25
p + .75
:
.05n - 2.00 +.50
.05n - 1.50
:
.10d + 1.25 + .75
.10d + 2.00
:
:
Hawthorne gives 4 half dollars to Priscilla, 3 half dollars to Nate, 2 half dolars to Dem, and 1 half dollar to Qasi,
.50h + 1.00 -(2.00+1.50+1.00+.50)
.50H + 1.00 - 5.00
.50h - 4.00
:
.01p+.75+2.00
.01p+2.75
:
.05n-1.50 + 1.50
.05n
:
.10d+2.00 + 1.00
.10d+3.00
:
.25q-2.50 + .50
.25q-2.00
they will all have the same amount of money. How many coins each start the problem with?
:
Resulting value expression for each type of coin
.01P+2.75
.05n
.10d+3.00
.25q-2.00
.50h-4.00
:
.05n = .10d+3.00; (they have the same amt of money)
"Nate has five times as many nickels as Dem has dimes."
n = 5d
therefore:
.05n = .10d + 3.00
.05(5d) = .10d + 3.00
.25d - .10d = 3.00
.15d = 3.00
d + 
d = 20 dimes
then
n = 5(20)
n = 100 nickels
:
Find p:
.01p + 2.75 = .05(100)
.01p + 2.75 = 5
.01p = 5 - 2.75
.01p = 2.25
p = 225 pennies
:
Find q, the same way
.25q - 2.00 = 5
.25q = 5 + 2
.25q = 7
q = 
q = 28 quarters
:
Find h
.50h - 4.00 = 5
.5h = 5 + 4
.5h = 9
h = 18 halfs
:
Summarize:
225 pennies
100 nickels
20 dimes
28 quarters
18 halfs
:
:
There is probably an easier way to do this, but I just can't come with it.
If you find a better way, would appreciate if you would let me know.
ankor@att.net
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