SOLUTION: I have 45 coins all in nickles and dimes. They total $3.10. How many of each do I have (nickles and dimes).

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Question 1066531: I have 45 coins all in nickles and dimes. They total $3.10. How many of each do I have (nickles and dimes).
Found 2 solutions by ikleyn, jim_thompson5910:
Answer by ikleyn(52799)   (Show Source): You can put this solution on YOUR website!
.
I have 45 coins all in nickles and dimes. They total $3.10. How many of each do I have (nickles and dimes).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let N be the number of nickels.
Then the number of dimes is (45-N).

Nickels contribute 5N cents to the total.

Dimes contribute 10*(45-N) cents to the total.

The "value" equation is

5N + 10*(45-N) = 310 cents.

5N + 450 - 10N = 310,

-5N = 310 - 450  --->  -5N = -140  --->  N=  = 28.

Answer. 28 Nickels and 45-28 = 17 dimes.

There is entire bunch of lessons on coin problems
    - Coin problems
    - More Coin problems
    - Solving coin problems without using equations
    - Kevin and Randy Muise have a jar containing coins
    - Typical coin problems from the archive
    - More complicated coin problems
    - Solving coin problems mentally by grouping without using equations
    - Santa Claus helps solving coin problem
in this site.

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

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Coin problems".


Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
n = number of nickels
d = number of dimes

We have 45 coins of nickels and dimes only, so,
n+d = 45
n = 45-d

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The value of the nickels is 5n cents while the value of all the dimes is 10d cents. In total, the value is 5n+10d. This must be set equal to 310 ($3.10 = 310 cents)

So we have this equation
5n+10d = 310

Plug in n = 45-d and solve for d
5n+10d = 310
5(n)+10d = 310
5(45-d)+10d = 310
5(45)+5(-d)+10d = 310
225-5d+10d = 310
225+5d = 310
225+5d-225 = 310-225
5d = 85
5d/5 = 85/5
d = 17

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Use this to find the value n

n = 45-d
n = 45-17
n = 28

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Summary:
n = 28 and d = 17
There are 28 nickels and 17 dimes
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