Question 1031663: A coin bank containing nickels, dimes and quarters has twenty eight coins in it, with a total value of $4.75. If the number of nickels and quarters combined is one more than twice the number of dimes, how many of each type coin is in the coin bank?
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! let n,d,q be the number of nickels, dimes and quarters respectively
n+d+q=28-------------1
5n+10d+25q=475
/5
n+2d+5q=95----------2
n+q=2d+1
n+q-2d=1-------------3
1 n + 1 d + 1 q = 28 -------------- 1
1 n + 2 d 5 q = 95 -------------- 2
1 n + -2 d + 1 q 1 -------------- 3
consider equation 1 &2 Eliminate d
Multiply 1 by -2 -5
Multiply 2 by 1 4
we get
-2 n + -2 d + -2 q = -56
1 n + 2 d + 5 q = 95
Add the two
-1 n + 0 d + 3 q = 39 ------------- 4
consider equation 2 & 3 Eliminate d
Multiply 2 by 1
Multiply 3 by 1
we get
1 n + 2 d + 5 q = 95
1 n + -2 d + 1 q = 1
Add the two
2 n + 0 d + 6 q = 96 -------------5 5
Consider (4) & (5) Eliminate n
Multiply 4 by 1
Multiply (5) by 1
we get
-1 n + 3 q = 39
2 n + 6 q = 96
Add the two
0 n + 9 q = 135
/ 9
q = 15
Plug the value of q in (5)
2 n + 6 z = 96
2 n = 6
n = 3
plug value of x & z in 1
3 + 10 d + 15 = 28
10 d = 28 + -3 + -15
d = 10
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