Question

Find three consecutive integers such that the sum of the second and triple the third is 193 more than the first.

a. n, n + 1, n + 2
b. n, n + 2, n + 4
c. n, n + 3, n + 6
d. n, n + 4, n + 8

Answer 1

The answer to the student's question is three consecutive integers: 62, 63, and 64. The correct representation for three consecutive integers is n, n + 1, n + 2 (option a). A simple algebraic equation solves the problem.

Step-by-step explanation:

The student is asked to find three consecutive integers such that the sum of the second and triple the third is 193 more than the first. We can express this situation using an algebraic equation based on the given options for consecutive integers. Option a, n, n + 1, n + 2, is the correct way to represent three consecutive integers.

Lets translate the word problem into an algebraic equation:
(n + 1) + 3(n + 2) = n + 193
This simplifies to:
n + 1 + 3n + 6 = n + 193
Combining like terms we get:
4n + 7 = n + 193
Subtract n from both sides:
3n + 7 = 193
Subtract 7 from both sides:
3n = 186
Divide by 3:
n = 62
The three consecutive integers are 62, 63, and 64.