Mary has $4.6 in nickels and dimes only. If she has fewer dimes than

We need to find the min value of nickels.

So let no of nickels = x
no of dimes = y

So the equation will be 5x+10y=460

First 3 answer choice will make the dimes more than nickels . So A,B,C are eliminated

D) 32*5 = 160

Nickel = 32 Dime = 30

E) 36*5=180
So Nickel = 36 and Dimes = 28

But we need to calculate min value of Nickel

So D is the correct choice.

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

To me the simpliest way is the following:

We know:

460 = 5X + 10Y -> 92 = X + 2Y
Y<X

First I calculate what would be the number of coins if x =y -> 92 = 3z -> z = 30.something (so if we had the same amount of nikels and dimes we would need 30+ coins).

I know that X = 92 -2Y (from the first equation), and I sustitute Y with 30 (as X will be more for sure since I got that from above)

X = 92-2*30 = 32.

D