Question

what is the smallest of three consecutive integers i the sum of the smaller two integers is two more than seven times the largest integers​

Answer 1

Answer:

The numbers that meet these conditions are -3, -2 and -1.

This means that the wording of the question is somewhat ambiguous:

The lowest of the three numbers is -3.

The smallest however is -1.

You may need clarification on which of those is being asked for.

Step-by-step explanation:

Let's call those numbers a, b and c, with a the smallest and c the largest. We're told two key things here:

1) The sum of the smaller two integers is two more than seven times the largest integer.  In other words a + b = 7c + 2

2) We're looking for three consecutive integers, which means that we can define them with a single variable.  If the smallest one is a, then the others are a + 1 and a + 2.

We can take those and put them together, giving us the equation:

a + (a + 1) =  7(a + 2) + 2

Which we can then solve for a:

a + (a + 1) =  7(a + 2) + 2

2a + 1 = 7a + 14 + 2

2a - 7a = 14 + 2 - 1

-5a = 15

a = -3

Since a is -3 and also the smallest, we can then say that the numbers are -3, -2 and -1.