Question 392072
A collection of 90 coins, pennies, nickels, and dimes, has a value of $2.85. If there are twice as may pennies as there are nickels and dimes combined, how many pennies, dimes, and nickels are there?
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x nickels
y dimes
z pennies
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z= 2(x+y)...................1
x+y+z=90.....................2
5x+10y+z=285.................3
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plug z in (2) & (3)
x+y+2(x+y) = 90
(x+y+x+y)= 90
3x+3y=90
/3
x+y = 30,,,,,,,,,,,,,,4
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5x+10y+z= 285
5x+10y +2(x+y) = 285
7x+12y=285,,,,,,,,,,,,,5
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multiply (4) by -7
we get
-7x-7y=-210

add to (5)
5y=75
y=15 dimes
from (4) x+y =30
x+15=30
x= 15 nickels
balance 15 are pennies
60 pennies, 15 dimes,15 nickels
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CHECK
60+150+75=285 
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m.ananth@hotmail.ca
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