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Question:-
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. Write and solve a system of equations to find old Fred and Natalie are ?
Solution:-
Let us assume that:-
- Natalie's age be 'x'
- Fred's age be 'y'
In Case 1 :-
It is given that => x + y = 44
So, x = 44 - y
In Case 2 :-
It is given that => 3x + y = 70
Now, putting the value of x in Case 2:-
»» 3x + y = 70
=> 3(44-y) + y = 70
=> 132 - 3y + y = 70
=> 132 - 2y = 70
=> -2y = 70 - 132
=> -2y = -62
=> 2y = 62
=> y = 62/2
=> y = 31
Then, Putting the value of y in Case 1:-
»» x + y = 44
=> x + 31 = 44
=> x = 44 - 31
=> x = 13
Hence,
- Natalie's age is 13
- Fred's age is 31
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