Find three consecutive integers such that the sum of the largest and five times the smallest is -244

Answer 1

Consider 3 consecutive integers: (smallest) x, x+1 and x+2 (largest)

Five times the smallest means 5x

Sum of the largest and five times the smallest means x+2+5x

This sum is -244 means x+2+5x=-244

Solve this equation

x+2+5x=-244

6x+2=-244

6x=-244-2

6x=-246

x=-41

So, smallest number is -41, second is -40 and largest is -39

You can check your answer now, -39+5(-41)=244

Answer 2

Let x=the smallest integer.

Then the second integer would be x+1 and the third (largest) integer would be x+2.

So five times the smallest integer is 5x.

The sum of the largest and five times the smallest is x+2+5x.

Set this expression equal to -244:

x+2+5x=-244

Combine like terms on the left side of the equation:

6x+2=-244

Subtract 2 from both sides of the equation:

6x=-246

Divide both sides of the equation by 6:

x=-41

So -41 is the first of the three consecutive integers.

The second consecutive integer is x+1 which is -41+1 which is -40.

The third consecutive integer is x+2 which is -41+2 which is -39.

So the three consecutive integers are -41,-40,-39.