SOLUTION: Robert has $14.60 in nickels, dimes, quarters and loonies. He has 4 times as many dimes as nickels, 3 times as many quarters as nickels and 3 less loonies than nickels. He has 69 c

Question 1158536: Robert has $14.60 in nickels, dimes, quarters and loonies. He has 4 times as many dimes as nickels, 3 times as many quarters as nickels and 3 less loonies than nickels. He has 69 coins all together. How many of each coin does he have? Answer algebraically and show your work.
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52858) (Show Source): You can put this solution on YOUR website!
.
Robert has $14.60 in nickels, dimes, quarters and loonies. He has 4 times as many dimes as nickels,
3 times as many quarters as nickels and 3 less loonies than nickels. He has 69 coins all together.
How many of each coin does he have? Answer algebraically and show your work.
~~~~~~~~~~~~~~~~~~~

Loonie is a Canadian one-dollar coin, introduced in 1987. Let x be the number of nickels. Then the number of dimes is 4x; the number of quarters 3x, and the number of loonies (x-3). The total for coins equation is x + 4x + 3x + (x-3) = 69. Simplify and find x 9x = 69 + 3 = 72 x = 72/9 = 8. ANSWER. 8 nickels, 4*8 = 32 dimes; 3*8 = 24 quarters and (8-3) = 5 loonies. CHECK for the total money : 8*0.05 + 32*0.10 + 24*0.25 + 5*1.00 = 14.60 dollars. ! Correct !

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Solved.

Note that of two conditions, one for total money and the other for total coins, ONE CONDITION IS EXCESSIVE.

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Nickels are 5c each
dimes are 10c each
quarters are 25c each
loonies?
Let = the value in cents of 1 loony
Let = number of nickels
Let = number of dimes
Let = number of quarters
-------------------------------------------
(1)
(2)
(3) number of loonies =
(4)
(5) ( in cents )
---------------------------------------------------------------
I have 4 unknowns and 4 equations, so it's solvable
Add (1) and (2)

Plug this result into (4)
(4)
(4)
(4)
(4)
and
(1)
(1)
(1)
and
(2)
(2)
(2)
and
Number of loonies =

He has:
8 nickels
32 dimes
24 quarters
5 loonies
-------------------------
(5) ( in cents )
(5) ( in cents )
(5) ( in cents )
(5)
(6)
A loony is worth 100c or $1

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