SOLUTION: A jar contains 50 nickels and dimes worth $4.30. How many of each kind of coin are in the jar?

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Question 970231: A jar contains 50 nickels and dimes worth $4.30. How many of each kind of coin are in the jar?
Found 3 solutions by AnlytcPhil, macston, Alan3354:
Answer by AnlytcPhil(1807) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of nickels be x
Then the number of dimes, using
ONE PART = TOTAL MINUS OTHER PART,
is 50-x.
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickels      x       $0.05    $0.05x
dimes      50-x      $0.10    $0.10(50-x)
-------------------------------------------
TOTALS      50        -----   $4.30

 The equation comes from the column on the right

  %28matrix%284%2C1%2CValue%2Cof%2CALL%2Cnickels%29%29%22%22%2B%22%22%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cdimes%29%29%22%22=%22%22%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoins%29%29

   0.05x + 0.10(50-x) = 4.30

Get rid of decimals by multiplying every term by 100:

        5x + 10(50-x) = 430

       5x + 500 - 10x = 430

            -5x + 500 = 430

                  -5x = -70

                    x = 14 = the number of nickels.

The number of dimes is 50-x or 50-14 or 36 dimes.

Checking:  14 nickels is $0.70 and 36 dimes is $3.60
            That's 50 coins.
            And indeed $0.70 + $3.60 = $4.30
Edwin

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
N=Number of nickels; D=number of dimes
N+D=50
D=50-N Use this to substitute for D below.
.
$0.05N+$0.10D=$4.30 (This converts number of coins to value) Substitute for D.
$0.05N+$0.10(50-N)=$4.30
$0.05N+$5.00-$0.10N=$4.30 Subtract $5.00 from each side.
-$0.05N=-$0.70 Divide each side by -$0.05.
N=14 ANSWER 1: There are 14 nickels in the jar.
.
D=50-N=50-14=36 ANSWER 2: There are 36 dimes in the jar.
.
CHECK:
$0.05N+$0.10D=$4.30
$0.05(14)+$0.10(36)=$4.30
$0.70+$3.60=$4.30
$4.30=$4.30

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A jar contains 50 nickels and dimes worth $4.30. How many of each kind of coin are in the jar?
============
A different method:
50 nickels = $2.50
Each dime adds 5 cents to the total
---
430 - 250 = 180
180/5 = 36 dimes
14 nickels