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 = [tex]x[/tex] years
The ages are consecutive integers.
So, age of the next older brother will be = [tex](x+1)[/tex] years
The age of the oldest brother will be = [tex](x+2)[/tex] years
The oldest brothers age is decreased by twice the youngest brother age.
The above statement can be represented as:
⇒ [tex](x+2)-2x[/tex]
Simplifying.
⇒ [tex]x-2x+2[/tex]
⇒[tex]-x+2[/tex]
The result for the above expression = -19.
So, we have:
[tex]-x+2=-19[/tex]
Subtracting both sides by 2.
[tex]-x+2-2=-19-2[/tex]
[tex]-x=-21[/tex]
Multiplying both sides by -1.
∴ [tex]x=21[/tex]
Thus, the youngest brother's age is 21 years
