Question

The total of three consecutive numbers is 210. what are the numbers. show all work

Answer 1

Let n = the first of three consecutive numbers.

Let n + 1 = the second consecutive number, and ...

Let n + 2 = the third consecutive number.

Since we're given that: "the sum of three consecutive numbers is 210," then we can now translate this statement mathematically into the following equation to be solved for the unknown number n:
n + (n + 1) + (n + 2) = 210

n + n + 1 + n + 2 = 210

Collecting like-terms on the left, we get:
3n + 3 = 210

3n + 3 - 3 = 210 - 3

3n + 0 = 207

3n = 207

(3n)/3 = 207/3

(3/3)n = 207/3

(1)n = 69

n = 69

Therefore, ,...
n + 1 = 69 + 1 = 70 and

n + 2 = 69 + 2 = 71

CHECK:
n + (n + 1) + (n + 2) = 210
69 + (70) + (71) = 210
69 + 70 + 71 = 210
210 = 210

Therefore, the three consecutive numbers whose sum is 210 are indeed 69, 70, and 71, and 71 is obviously the largest of these three numbers