Respuesta :
Answer:
Fred is 31 years old and Natalie is 14 years old.
Step-by-step explanation:
Given:
If you add Natalie's age and Fred's age, the result is 45.
If you add Fred's age to 3 times Natalie's age, the result is 73.
Now, to find the age of Fred and Natalie.
Let the age of Fred be [tex]x.[/tex]
And the age of Natalie be [tex]y.[/tex]
As, given If you add Natalie's age and Fred's age, the result is 45.
[tex]x+y=45[/tex] ......(1)
Now, if you add Fred's age to 3 times Natalie's age, the result is 73.
[tex]x+3y=73[/tex] ......(2)
So, to solve the equations by using elimination method.
Now, subtracting both the equations (1) and (2):
[tex]x+y-(x+3y)=45-73[/tex]
[tex]x+y-x-3y=-28[/tex]
[tex]-2y=-28[/tex]
Dividing both sides by -2 we get:
[tex]y=14.[/tex]
Natalie's age = 14 years.
Now, to get the age of Fred by substituting the value of [tex]y[/tex] in equation (1):
[tex]x+y=45\\\\x+14=45[/tex]
Subtracting both sides by 14 we get:
[tex]x=31.[/tex]
Fred age = 31 years.
Therefore, Fred is 31 years old and Natalie is 14 years old.
