Question

If you add​ natalie's age and​ fred's age, the result is 39. if you add​ fred's age to 3 times​ natalie's age, the result is 65. write and solve a system of equations to find how old fred and natalie are.

Answer 1

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Answer 2

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Define x and y :
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Let Natalie's age be x.
Let Fred's age be y.

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Construct equations:
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Add​ Natalie's age and​ Fred's age, the result is 39
⇒ x + y = 39

Add​ Fred's age to 3 times​ Natalie's age, the result is 65.
⇒ y + 3x = 65

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Solve x and y :
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x + y = 39 -------------- (1)
y + 3x = 65 ------------ (2)

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From Equation (1) :
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x + y = 39
x = 39 - y

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Sub x = 39 - y into equation (2) :
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y + 3x = 65
y + 3(39 - y) = 65
y + 117 - 3y = 65
2y = 52
y = 26

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Sub y = 26 into equation 1 :
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x = 39 - 26
x = 13

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Find their age :
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Natalie = x = 13
Fred = y = 26

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Answer : Natalie is 13 years old and Fred is 26 years old.
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