SOLUTION: there were 24 nickles, dimes, and quarters whose total value equaled $4.25. how many coins of each kind were there if the number of nickels equaled the number of dimes?

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Question 1179758: there were 24 nickles, dimes, and quarters whose total value equaled $4.25. how many coins of each kind were there if the number of nickels equaled the number of dimes?
Found 4 solutions by mananth, greenestamps, josgarithmetic, ikleyn:
Answer by mananth(16949) About Me  (Show Source):
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there were 24 nickles, dimes, and quarters whose total value equaled $4.25.
n+d+q=24
5n+10d+25q= 425
n=d

n+d+q=24
d+d+q=24
2d+q=24
5n+10d+25q= 425
5d+10d+25q=425
15d+25q =425
d dimes
q quarters


2.00 d + 1.00 q = 24.00


15.00 d + 25.00 q = 425.00 .............2
Eliminate q
multiply (1)by -25.00
Multiply (2) by 1.00
-50.00 d -25.00 q = -600.00
15.00 d 25.00 q = 425.00
Add the two equations
-35.00 d = -175.00
/ -35.00
d = 5.00
plug value of d in (1)
2.00 d + 1.00 q = 24.00
10.00 + 1.00 q = 24.00
1.00 q = 14.00
q = 14.00
Ans d = 5
q = 14
5 dimes
14 quarters


Answer by greenestamps(13276) About Me  (Show Source):
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Let x = # of nickels
Then x = # of dimes (same as the number of nickels)
And then 24-2x = # of quarters (the total number of coins is 24)

The total value of the coins is $4.25, or 425 cents:

5%28x%29%2B10%28x%29%2B25%2824-2x%29=425
15x%2B600-50x=425
175=35x
x=5

ANSWERS:
nickels: x = 5
dimes: x = 5
quarters: 24-2x=14

CHECK: 5(5)+10(5)+25(14)=25+50+350=425

Answer by josgarithmetic(39711) About Me  (Show Source):
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how many coins of each kind were there if the number of nickels equaled the number of dimes?
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x nickels and x dimes,

5x%2B10x%2B25%2824-2x%29=425
.
.

Answer by ikleyn(53538) About Me  (Show Source):
You can put this solution on YOUR website!
.
there were 24 nickles, dimes, and quarters whose total value equaled $4.25.
how many coins of each kind were there if the number of nickels equaled the number of dimes?
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        Here is very simple way to solve this problem for 3 unknowns using only one equation. 


Let x be the number of nickels.

Then the number of dimes also is x, according to the problem.


Then the number of quarters is  24-x-x = 24-2x.


Now write the total money equation

    5x + 10x + 25*(24-2x) = 425  cents.


Simplify and find x

    15x + 600 - 50x = 425

    600 - 425 = 50x - 15x

       175    =    35x

         x    =     175/35 = 5.


ANSWER.  5 nickels, 5 dimes and 24-5-5 = 14 quarters.


CHECK  for the total money  5*5 + 5*10 + 14*25 = 425 cents.   ! correct !

Solved completely, using only one equation.