Mary has $4.6 in nickels and dimes only. If she has fewer dimes than nickels, what is the least possible number of nickels she could have?

(A) 24

(B) 27

(C) 30

(D) 32

(E) 36
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Hi Afc0892,

A Nickel is 5 cents and a Dime is 10 Cents , so 10x+5y=460 cents , where x is number of dimes and y is number of Nickels. Now please try to solve.

Hope this helps!
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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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