SOLUTION: I have 30 coins, all nickels, dimes, and quarters worth $4.60. There are three times as many quarters as nickels and two more dimes than quarters. How many of each kind of coin d

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: I have 30 coins, all nickels, dimes, and quarters worth $4.60. There are three times as many quarters as nickels and two more dimes than quarters. How many of each kind of coin d      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 31487: I have 30 coins, all nickels, dimes, and quarters worth $4.60. There are three times as many quarters as nickels and two more dimes than quarters. How many of each kind of coin do I have?
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
1. +Q+%2B+N+%2B+D+=+30+ I have 30 coins, all nickels, dimes, and quarters
2. +N+=+1Q%2F3+ three times as many quarters as nickels
3. +D+=+Q+%2B+2+ two more dimes than quarters
4. +.25Q+%2B+.05N+%2B+.10D+=+4.60+ nickels, dimes, and quarters worth $4.60.
Take the 2nd and third equations and substitute them into the first.
+1Q+%2B+1Q%2F3+%2B+1Q+%2B+2+=+30+ combine like terms
+7Q%2F3+%2B+2+=+30+
+7Q%2F3+=+28+ multiply both sides by 3/7
+%287Q%2F3%29%283%2F7%29+=+28%283%2F7%29+
+Q+=+12+ Plug this into the second and third equations
+N+=+1%2812%29%2F3+ snd +D+=+12+%2B+2+
+N+=+4+ and +D+=+14+
plug the value of Q, N and D into the first equation
+Q+%2B+N+%2B+D+=+30+
+12+%2B+4+%2B+14+=+30+
+30+=+30+ TRUE!!
Now plug all three into the 4th equation
+.25Q+%2B+.05N+%2B+.10D+=+4.60+
+.25%2812%29+%2B+.05%284%29+%2B+.10%2814%29+=+4.60+ Multiply
+3+%2B+0.20+%2B+1.40+=+4.60+ add
+4.60+=+4.60+ TRUE
Q = 12
D = 14
N = 4