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A coin collection is made up of 34 coins comprised of nickels and dimes. The total value of the collection is $1.90. How many dimes and nickels made up these collections?

 Feb 9, 2020
 #1
avatar+21931 
+1

Nickles = x

   then dimes =  34-x

 

 

.05 x    + .10  ( 34-x)   = 1.90      solve for 'x' the number of nickles     then dimes = 34-x

 Feb 9, 2020
 #2
avatar+24388 
+1

A coin collection is made up of 34 coins comprised of nickels and dimes.
The total value of the collection is $1.90.
How many dimes and nickels made up these collections?

 

\(\begin{array}{|lrcll|} \hline (1) & 5n+10d &=& 190 \\ \hline (2) & n + d &=& 34 \quad | \quad \times 5 \\ & 5n+5d &=& 170 \\ \hline (1)-(2): & 5n+10d -(5n+5d) &=& 190-170 \\ & 5n+10d -5n-5d &=& 20 \\ & 10d -5d &=& 20 \\ & 5d &=& 20 \quad | \quad : 5 \\ & \mathbf{d} &=& \mathbf{4} \\ \hline & n+d &=& 34 \quad | \quad d = 4 \\ & n+4 &=& 34 \\ & n &=& 34 - 4 \\ & \mathbf{n} &=& \mathbf{30} \\ \end{array}\)

 

There are 30 nickels and 4 dimes in these collections.

 

laugh

 Feb 9, 2020

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