SOLUTION: Hello, may you please help me on this problem. N of the 34 coins are quarters. The rest are nickels. The total value of the coins are $5.30. What is N? Thank you! Please show

Algebra ->  Equations -> SOLUTION: Hello, may you please help me on this problem. N of the 34 coins are quarters. The rest are nickels. The total value of the coins are $5.30. What is N? Thank you! Please show      Log On


   

Question 720847: Hello, may you please help me on this problem.
N of the 34 coins are quarters. The rest are nickels. The total value of the coins are $5.30. What is N?
Thank you! Please show work so I can understand this problem more. Thank you again!

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Let +n+ = number of nickels
Let +N = number of quarters
given:
+N+%2B+n+=+34+....eq.1
++0.25N+%2B0.05n=+5.30+....eq.2
------------------------
solve ....eq.1 for +N+
+N+=+34-n+
and substitute it in ....eq.2
+0.25%2834-n%29+%2B0.05n=+5.30+....eq.2...solve for +n+
+8.5-+0.25n%2B0.05n=+5.30+
+8.5-+0.20n=+5.30+
+8.5-+5.30+=0.20n
+3.2+=0.20n
+n=3.2+%2F0.20
+n=16
and, since
+N+%2B+n+=+34+
+N+%2B+16+=+34+
+N+=+34+-16
+N+=+18
The number of nickels is 16
The number of quarters is 18
check:
+N+%2B+n+=+34+....eq.1
+18%2B+16=+34+
+34=+34+
++0.25N+%2B0.05n=+5.30+....eq.2
++0.25%2A18+%2B0.05%2A16=+5.30+
++4.50+%2B0.80=+5.30+
++5.30=+5.30+