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Let, the numbers of nickels be x.
Given, there were 5 times as many dimes as nickels.
So, the number of dimes = 5x
We know that 1 nickel = $(0.05)
So x nickels = $(0.05x)
Also we know that 1 dime = $(0.1)
So 5x dimes = $(0.1 ×5x) = $(0.5x)
Given total value of dimes and nickels at the end of day 1 is $63.80
So we can write the equation
Now we to find x, we have to move 0.55 to the other side. As 0.55 is multiplied there so to move it we need to divide it to both sides.
So we have got the number of nickels = 116
Number of dimes = 5x = 5(116) = 580
So we have got the required answer.
Number of nickels = 116, number of dimes = 580.