Question 656591: Hank has a pocketful of nickels, dimes, and quarters. He has 18 coins in all, worth $2.00. Find how many of each coin he has if he has twice as many dimes as nickels?
I tried setting up a chart but i didn't know what to put for the quarters box and amount of item column.
Answer by MathTherapy(10555)   (Show Source):
You can put this solution on YOUR website! Hank has a pocketful of nickels, dimes, and quarters. He has 18 coins in all, worth $2.00. Find how many of each coin he has if he has twice as many dimes as nickels?
I tried setting up a chart but i didn't know what to put for the quarters box and amount of item column.
Let the amount of nickels, dimes, and quarters be N, D, and Q, respectively
Then: N + D + Q = 18 ----- eq (i)
Also, D = 2N ---- eq (ii)
N + 2N + Q = 18 ---- Substituting 2N for D in eq (i) ---- 3N + Q = 18 ---- eq (iii)
Since value of all coins = $2, then: .05N + .1(2N) + .25Q = 2 ---- .25N + .25Q = 2 ----- eq (iv)
We now have: 
- .75N - .25Q = - 4.5 ------ Multiplying eq (iii) by - .25 ----- eq (v)
.25N + .25Q = 2 ------ eq (iv)
- .5N = - 2.5 ----- Adding eqs (v) & (iv)
N, or amount of nickels =  , or 
D = 2(5) ---- Substituting 5 for N in eq (ii)
D, or amount of dimes = 
3(5) + Q = 18 ---- Substituting 5 for N in eq (iii)
15 + Q = 18
Q = 18 - 15
Q, or amount of quarters = 
I'll leave the check up to you!!!
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