If you add​ Natalie's age and​ Fred's age, the result is 44. If you add​ Fred's age to 3 times​ Natalie's age, the result is 70.

Question

Write and solve a system of equations to find how old Fred and Natalie are.

Answer 1

Let Natalie's Age be x

Let Fred's age be y

Equation 1: x + y = 44

Equation 2: 3x + y = 70

Based on Equation 1: x + y = 44

Therefore x = 44 - y

Now substitute x in equation 2:

3(44 - y) + y = 70

132 - 3y + y = 70

132 - 2y = 70

-2y = 70 - 132

-2y = -56

2y = 62

y = 62/2

y = 31.

put value of y back in equation 1

x + y = 44

x + 31 = 44

x = 44-31

x = 13

Thus Natalie's Age is 13 & Fred's Age is 31