Question 1051865
.
A coin bank contains only nickels and dimes. The total value of the coins in the bank is $3.50. 
If the nickels were dimes and the dimes were nickels, the total value of the coins would be $2.50. 
Find the number of nickels in the bank.
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<pre>
Let n be the number of nickels and d be the number of dimes.

Then 

5n + 10d = 350 cents   (1)    ("The total value of the coins in the bank is $3.50. ")
10n + 5d = 250 cents   (2)    ("If the nickels were dimes and the dimes were nickels, the total value of the coins would be $2.50")

Cancel the factor 5 in both sides of both equations. You will get

n + 2d = 70            (3)
2n + d = 50            (4)

From (3), express n = 70-2d and substitute it into (4). You will get

2*(70-2d) + d = 50.

Simplify and solve for d:

140 - 4d + d = 50,  or

-3d = 50 - 140  --->  -3d = -90  --->  d = 30.

Thus the number of dimes is 30.

Then the number of nickels, from (3), is n = 70-2d = 70 - 2*30 = 10.

Check it on your own.

<U>Answer</U>.  30 dimes and 10 nickels.
</pre>

There is entire bunch of the lessons on coin problems

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/coins/Coin-problems.lesson>Coin problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/coins/More-Coin-problems.lesson>More Coin problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/coins/Solving-coin-problem-without-equations.lesson>Solving coin problems without using equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/coins/Kevin-and-Randy-Muise-have-a-jar.lesson>Kevin and Randy Muise have a jar containing coins</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/coins/Typical-coin-problems-from-the-archive.lesson>Typical coin problems from the archive</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/coins/More-complicated-coin-problems.lesson>More complicated coin problems</A>

in this site.


Read them and become an expert in solution of coin problems.


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