SOLUTION: Emily has a total of 20 dimes and nickels. The total amount she has is $1.60. How many of each coin does she have?

Algebra.Com
Question 927750: Emily has a total of 20 dimes and nickels. The total amount she has is $1.60. How many of each coin does she have?
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Emily has a total of 20 dimes and nickels. The total amount she has is $1.60. How many of each coin does she have?
Let the number of nickels be x
Then the number of dimes, using
ONE PART = TOTAL MINUS OTHER PART,
is 20-x.
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
NICKELS      x        $0.05    $0.05x
DIMES      20-x       $0.10    $0.10(20-x)
-------------------------------------------
TOTALS      20        -----    $1.60

 The equation comes from the column on the right

  

0.05x + 0.10(20-x) = 1.60

Get rid of decimals by multiplying every term by 100

     5x + 10(20-x) = 160

    5x + 200 - 10x = 160

         -5x + 200 = 160

               -5x = -40

                 x = 8 = the number of nickels

The number of dimes is 20-x or 20-8 or 12 dimes.

Checking:  8 nickels is $0.40 and 12 dimes is $1.20

And indeed $0.40+$1.20 = $1.60.

Edwin
RELATED QUESTIONS

Emily has the same number of nickels and dimes. The coins total $2.55.How many of each... (answered by stanbon)
1. Mary has $2.25 in coins. She has the same number of quarters as dimes. She has half as (answered by ankor@dixie-net.com)
Selena has some nickels, dimes and quarters. She has 1½ times as many dimes as nickels.... (answered by josgarithmetic,macston,MathTherapy)
Emily has nickels, dimes, and quarters in her piggy bank. She has twice as many dimes as... (answered by ankor@dixie-net.com)
Emily has nickels, dimes, and quarters in her piggy bank. She has twice as many dimes as (answered by Fombitz)
If Brianna has 4 times the amount of nickels as she does dimes and the total amount is... (answered by ewatrrr)
a Woman has 11 coins, consisting of nickels and dimes. she has three more dimes than... (answered by josmiceli)
Adriana has 24 dimes and nickels in a jar. The total value of the coins in the jar is... (answered by math_helper)
Danielle has nickels, dimes and quarters. She has a total of $33.60. She has four times... (answered by edjones)