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.
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 + {{{3/.15}}}
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 = {{{7/.25}}}
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