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(52855)   (Show Source):
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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.
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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):
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