Question

The ages of 3 brothers are represented by consecutive integers. If the oldest brothers age is decreased by twice the youngest brother age the result is -19. How old is the youngest brother

Answer 1

Answer:

The youngest brother's age is 21 years.

Step-by-step explanation:

Given:

The ages of 3 brothers are consecutive integers.

If the oldest brothers age is decreased by twice the youngest brother age the result is -19

To find the age of the youngest brother.

Solution:

Let the age of youngest broth be = $x$  years

The ages are consecutive integers.

So, age of the next older brother will be = $(x+1)$ years

The age of the oldest brother will be = $(x+2)$ years

The oldest brothers age is decreased by twice the youngest brother age.

The above statement can be represented as:

⇒ $(x+2)-2x$

Simplifying.

⇒ $x-2x+2$

⇒$-x+2$

The result for the above expression = -19.

So, we have:

$-x+2=-19$

Subtracting both sides by 2.

$-x+2-2=-19-2$

$-x=-21$

Multiplying both sides by -1.

∴ $x=21$

Thus, the youngest brother's age is 21 years