SOLUTION: angelina has collection of nickels and dimes worth &4.65. if she has 70 nickels and dimes, how many of each does she have?

Question 1034899: angelina has collection of nickels and dimes worth &4.65. if she has 70 nickels and dimes, how many of each does she have?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

Let the number of nickels be x
Let the number of dimes be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickels      x      $0.05       $0.05x
dimes        y      $0.10       $0.10y
-------------------------------------------
TOTALS      70      -----       $4.65

 The first equation comes from the "number of coins" column.

   

                   x + y = 70

 The second equation comes from the last column.
  

           0.05x + 0.10y = 4.65

Get rid of decimals by multiplying every term by 100:

                5x + 10y = 465

 So we have the system of equations:
           .

We solve by substitution.  Solve the first equation for y:

                  x + y = 70
                      y = 70 - x

Substitute (70 - x) for y in 5x + 10y = 465

        5x + 10(70 - x) = 465
         5x + 700 - 10x = 465
              -5x + 700 = 465
                    -5x = -235
                 x = 47 = the number of nickels.

Substitute in y = 70 - x
              y = 70 - (47)
              y = 23 dimes.

Checking:  47 nickels is $2.35 and 23 dimes is $2.30
            That's 70 coins.
            And indeed $2.35 + $2.30 = $4.65
Edwin

RELATED QUESTIONS
angelina has a collection of nickels and dimes worth $4.75. If she has 70 dimes and... (answered by ikleyn)

angelina has a collection of nickels and dimes worth $4.75. If she has 70 dimes and... (answered by ikleyn)

Angelina has a collection of nickels and dimes worth $4.65. If she has 70 nickels and... (answered by josgarithmetic,MathTherapy,ikleyn)

Keisha has a collection of dimes and nickels worth a total of $4. If she has 50 coins in... (answered by sck12,Alan3354)

Rita has a collection of 82 dimes and nickels worth $6.65. How many nickels does she... (answered by macston)

Joan has $1.75 worth of change in nickels and dimes if she has three times as many... (answered by Alan3354)

Sarah has a collection of nickels, dimes, and quarters worth $15.75. She has 10 more... (answered by ankor@dixie-net.com)

Sara has a collection of nickels, dimes, and quarters, worth $15.75. She has 10 more... (answered by stanbon)

Sarah has a coin collection of nickels, dimes, and quarters worth $15.75. She has 10 more (answered by josmiceli)