Question

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.

Answer 1

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