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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