Find three consecutive integers such that the sum of the first and twice the second is 80 minus three times the third

The three consecutive integers are 12, 13, 14.

Step-by-step explanation:

Encode the question in an equation. We are given two facts: (1) the three integers are consecutive, and (2) they relate to each other through a sum.

Pick any of the integers (first, second, or third) and call it n. Then write the two others correspondingly in terms of n. I pick the middle one as n, so the three consecutive integers are (n-1), n, (n+1). That's (1). As for (2), here is the fact:

Lo and behold, one equation with one unknown! Easy to solve for n to give us  the middle integer, n:

The three consecutive integers are 12, 13, 14.

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6 meters

step-by-step explanation: