Question 224690
A collection of nickels and dimes contains 6 more dimes than nickels. The total value of the collection is $1.95. How many nickels are there in the collection?


Step 1.  Let x be the number of nickels.


Step 2.  Let 0.05x be the dollar value of nickels.


Step 3.  Let y be the number of dimes.


Step 4.  Let 0.10y be the dollar value of dimes.


Step 5.  Then 0.05x+0.10y=1.95 be the total dollar value.


Step 6.  Also, y=x+6  since there are 6 more dimes than nickels


Step 7.  Our linear system of equation is given in Steps 4 and 5 shown below:


{{{0.05x+0.10y=1.95}}}
{{{-x+y=6}}}


*[invoke linear_substitution "x", "y", .05, 0.10, 1.95, -1, 1, 6 ]


So x=9 and y=15.  Note there are 6 more dimes than quarters. and the total dollar value is 0.05*9+0.10*15=0.45+1.50=1.95 which is a true statement.


Step 8.  ANSWER:  The number of nickels is 9 and the number of dimes is 15.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J