1 Nickel = 5 cents, Let Mary have x nickels

1 Dime = 10 cents, let Mary have y dimes

Total amount = 460 cents

We get the equation 5x + 10y = 460

x + 2y = 92

Note that the coefficients are co-prime

First value that satisfies is x = 2, y= 45

After these the subsequent values of x are obtained by adding 2(coefficient of y in the equation) to the previous value

So, x = 2,4,6,8,.... which is an A.P

Similarly the subsequent values of y are obtained by subtracting 1(coefficient of x in the equation) to the previous value

So, y= 45,44,43,42,.... which is an A.P

Now it is given that x > y

Let it happen for the nth term of each A.P

2n > 45 - (n - 1 )

3n > 46

n > 15.33

i.e 16th term

number of nickels = 32 ; number of dimes = 30

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