Final answer:
The largest prime number, p, such that 9 times p is less than 400, is option c, 43, because 43 multiplied by 9 equals 387, which is less than 400.
Step-by-step explanation:
We need to find the largest prime number, p, such that when multiplied by 9 it is less than 400. This can be formulated as 9p < 400.
First, we divide 400 by 9 to find the upper limit for p:
400 / 9 ≈ 44.44
Since we need a prime number and it must be less than 44.44, we look for the nearest prime number that is less than that value. Checking the given options:
- Option a: 37 × 9 = 333
- Option b: 41 × 9 = 369
- Option c: 43 × 9 = 387
- Option d: 47 × 9 = 423
Option d is too large since 47 × 9 exceeds 400. Between the remaining options, option c, which is 43, is the largest prime number that satisfies the condition 9p < 400. Thus, the correct answer is c. 43.