SOLUTION: Find the number of nickels, dimes, and quarters in a collection of 80 such coins if the nickels and the quarters are worth $4.50 and the value of the quarters and the dimes is $5.5

Question 933517: Find the number of nickels, dimes, and quarters in a collection of 80 such coins if the nickels and the quarters are worth $4.50 and the value of the quarters and the dimes is $5.50.
My work:
.5n + .25q = 4.50
.10d + .25q = 5.50
.10d - .5n = 1.00
n + .5q = 9
d + 2.5q = 55
d - 5n = 10
d + n + q = 80 coins
Ive tried everything, even made a chart - please help!!
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the number of nickels, dimes, and quarters in a collection of 80 such coins if the nickels and the quarters are worth $4.50 and the value of the quarters and the dimes is $5.50.
------
Quantity:: n + d + q = 80 coins
Value:: 5n + 25q = 450 cents
Value:: 10d + 25q = 550 cents
--------------------------------
Using the bottom 2 equations,
Subtract and solve for 10d-5n::
10d-5n = 100
Modify::
2d - n = 20
n = 2d-20
---
Substitute for "n" in equation #1 to get::
2d-20 + d + q = 80
3d + q = 100
q = -3d+100
----
Substitute for "n" and for "q" in 5n+25q=450 to solve for "d"
5(2d-20) + 25(-3d+100) = 450
10d - 100 -75d + 2500 = 450
-65d = 450-2400
-65d = -1950
d = 30 (# of dimes)
----
Solve for "q" using q = -3d+100
q = -3*30+100 = 10 (# of quarters)
----
Solve for "n" using n = 2d-20
n = 2*30-20 = 40 (# of quarters)
----
Checking with the 1st equation:
30 + 10 + 40 = 80 coins
-----
Cheers,
Stan H.
----------------
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

,
, and

given:
.....eq.1
if the nickels and the quarters are worth $
.....eq.2
the value of the quarters and the dimes is $
.....eq.3

solve the system:
.....eq.1
.....eq.2
.....eq.3
_________________________________
.....eq.2...multiply by
.....eq.3...multiply by
____________________________
.....eq.2
.....eq.3
__________________________________

.....eq.1..solve for
.......substitute in eq.2

.....eq.2 ...

...solve for

...................

go to .....eq.3....substitute

go to . ........substitute and find

go to
.......substitute and , find

RELATED QUESTIONS
In a coin collection there are Nickels, Dimes, and Quarters. If the total number of coins (answered by stanbon)
A collection of nickels, dimes, and quarters consist of 95 coins with a total of $ (answered by ikleyn)
A collection of 72 coins is worth $7.20. There are 12 more nickels than dimes and the... (answered by josgarithmetic)
A collection of nickels, dimes and quarters is worth $5.30. There are two more dimes... (answered by ikleyn)
A collection of nickels dimes and quarters amount to $10.00 there are 140 coins and there (answered by ikleyn)
In a collection of coins there are twice as many nickels as dimes and 7 less quarters... (answered by mananth)
A collection of 21 nickels, dimes, and quarters is worth $2.50. There are five fewer... (answered by jorel1380)
A collection of nickels, dimes, and quarters amounts to $10.00. If there are 140 coins in (answered by edjones)
A collection of nickels, dimes, and quarters amounts to $10.00. If there are 140 coins in (answered by edjones)