if you add natalie's age and fred's age, the result is 46. if you add fred's age to 3 times natalie's age, the result is 76. write and solve a system of equations to find how old fred and natalie are.

The age of Fred is 31 years old and age of Natalie is 15 years old

Solution:

Let the age of fred be "x"

Let the age of natalie be "y"

If you add Natalie's age and Fred's age, the result is 46

Therefore,

Age of Natalie + Age of Fred = 46

x + y = 46 eqn 1

If you add Fred's age to 3 times Natalie's age, the result is 76

Age of Fred + 3 times the Age of Natalie = 76

x + 3y = 76 eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 46 - y eqn 3

Substitute eqn 3 in eqn 2

46 - y + 3y = 76

46 + 2y = 76

2y = 76 - 46

2y = 30

y = 15

Substitute y = 15 in eqn 3

x = 46 - 15

x = 31

Thus age of Fred is 31 years old and age of Natalie is 15 years old

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2