SOLUTION: A coin collection consists of 14 coins with a value of $1.35. The coins are nickels, dimes, and quarters. The numbers of nickles is three less than twice the number of dimes. How m
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Question 171118: A coin collection consists of 14 coins with a value of $1.35. The coins are nickels, dimes, and quarters. The numbers of nickles is three less than twice the number of dimes. How many of each coin is there in the collection Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! Let x=number of nickels
y=number of dimes
z=number of quarters
Lets deal in pennies; we are told that:
5x+10y+25z=135---------------------eq1
x+y+z=14-----------------------------eq2
and
x=2y-3-------------------------------eq3
multiply eq2 by 25 (we get: 25x+25y+25z=350) and subtract eq1 from it and we get:
20x+15y=215---------------------eq2a
substitute x=2y-3 from eq3 into eq2a:
20(2y-3)+15y=215 simplifying we get:
40y-60+15y=215 add 60 to each side
55y=275 divide each side by 5
y=5 -------------------------------------number of dimes
From eq3:
x=2y-3=2*5-3=7------------------------------number of nickels
substitute x=7 and y=5 into eq2 and we get:
7+5+z=14
z=2--------------------------------------------number of quarters
CK
7+5+2=14
14=14
and
7*5+10*5+2*25=135
35+50+50=135
135=135
