Question

select the correct answer.
currently, nora is 3 times as old as damon. in 8 years, she will only be 2 times as old as damon. how old will damon be in 8 years?
a. 8 years old
b. 16 years old
c. 24 years old
d. 32 years old

Explanation:

Step1: Define variables

Let Damon's current age be \( x \). Then Nora's current age is \( 3x \).

Step2: Set up equation for 8 years later

In 8 years, Damon's age will be \( x + 8 \) and Nora's age will be \( 3x + 8 \). We know that in 8 years, Nora will be 2 times as old as Damon, so we can write the equation:

$$ 3x + 8 = 2(x + 8) $$

Step3: Solve the equation

First, expand the right - hand side:

$$ 3x + 8 = 2x + 16 $$

Subtract \( 2x \) from both sides:

$$ 3x - 2x+ 8=2x - 2x + 16 $$

$$ x + 8=16 $$

Subtract 8 from both sides:

$$ x=16 - 8=8 $$

Step4: Find Damon's age in 8 years

Damon's current age \( x = 8 \). In 8 years, his age will be \( 8 + 8=16 \) years old.

Answer:

B. 16 years old