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?
+36916 Nickles = x
then dimes = 34-x
.05 x + .10 ( 34-x) = 1.90 solve for 'x' the number of nickles then dimes = 34-x
+26367 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.
