20) Solve the problem. Suppose that 12 unique names are put into a hat and drawn at random without
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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:
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.