For all nonnegative integers a, b, and c, the function G is defined by

We are given that the function G is defined by G(a,b,c) = 7^2*a + 7^1*b + 7^0*c = 49a + 7b + c and need to determine which answer choice is equal to G(5,4,1) – G(3,6,4).

G(5,4,1) = 49(5) + 7(4) + 1 = 274

G(3,6,4) = 49(3) + 7(6) + 4 = 193

G(5,4,1) – G(3,6,4) = 274 – 193 = 81

Although we could go through each answer choice and see which one will yield the result of 81, an easier approach is to express 81 in the form of 49a + 7b + c. That is, if 81 = 49a + 7b + c, what are the values of a, b, and c? Keep in mind that a, b, and c are nonnegative integers.

81 = 49a + 7b + c

Since 81 is more than 49 but less than 2 times 49, a must be 1. In that case, we have:

81 = 49(1) + 7b + c

81 = 49 + 7b + c

32 = 7b + c

Since 32 is more than 4 times 7 but less than 5 times 7, b must be 4. In that case, we have:

32 = 7(4) + c

32 = 28 + c

4 = c

Therefore, a = 1, b = 4, and c = 4. In other words, 81 = 49(1) + 7(4) + 4.

However, 49(1) + 7(4) + 4 = G(1, 4, 4), so 81 = G(1, 4, 4).

Answer: B