Final answer:
By setting up a system of equations with the given times for sums and products and using substitution or elimination, we can solve for the time taken to perform one sum and one product. Upon calculation, it takes approximately 8.092 nanoseconds to carry out one sum and one product, which rounds to 8 nanoseconds, Answer D.
Step-by-step explanation:
The student's question can be approached by setting up a system of equations to solve for the time it takes for one sum (S) and one product (P) to be carried out by the computer. We are provided with two scenarios:
- 3S + 8P = 47 nanoseconds
- 2S + 9P = 48 nanoseconds
To find the values of S and P, we can use substitution or elimination. If we multiply the first equation by 2 and the second equation by 3, we get:
- 6S + 16P = 94 nanoseconds (Equation A)
- 6S + 27P = 144 nanoseconds (Equation B)
Subtract Equation A from Equation B to eliminate S:
Now we divide both sides by 11 to get the time taken for one product (P):
- P = 50 / 11 nanoseconds = approximately 4.545 nanoseconds
Using the original first equation to solve for S, substituting the value of P:
- 3S + 8(4.545) = 47
- 3S + 36.36 = 47
- 3S = 47 - 36.36
- 3S = 10.64
- S = 10.64 / 3 nanoseconds = approximately 3.547 nanoseconds
Adding the time for one sum and one product, we get S + P which is approximately 3.547 + 4.545 = 8.092 nanoseconds. The answer is closest to 8 nanoseconds, so the correct choice is
D) 8 nanoseconds
.