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If you add​ Natalie's age and​ Fred's age, the result is 39. If you add​ Fred's age to 4 times​ Natalie's age, the result is 78. Write and solve a system of equations to find how old Fred and Natalie are.

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Step-by-step explanation:

We can write this word problem as two variables. Let us assume that:

x = Natalie's age

y = Fred's age

The first part of the word problem is that "If you add​ Natalie's age and​ Fred's age, the result is 39." Therefore:

Natalie's age + Fred's age = 39

x + y = 39

This will be our first equation. The second equation can be derived from the statement that "If you add​ Fred's age to 4 times​ Natalie's age, the result is 78." Therefore:

(4 times Natalie's age) + Fred's age = 78

4x + y = 78

We can now form a system of equations and solve for both x and y:

[tex]\left \{ {{x + y = 39} \atop {4x + y = 78}} \right.[/tex]

The simplest way to solve would be using the Substitution method, as seen here:

x + y = 39

y = 39 - x

4x + y = 78

4x + (39 - x) = 78

3x + 39 = 78

3x = 39

x = 13

x + y = 39

13 + y = 39

y = 26

Remember that x = Natalie's age and y = Fred's age. Therefore, Natalie's age is 13 years old and Fred's age is 26 years old.

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