Solve the riddle.

Question

Dividing my dog’s age by 4 and adding 6 is the same as dividing my dog’s age by 8 and adding 8.

StartFraction x Over 4 EndFraction + 6 = StartFraction x Over 8 EndFraction + 8

How old is my dog?

years old

Answer 1

Let's solve the riddle step by step.

We have the equation:

\[ \frac{x}{4} + 6 = \frac{x}{8} + 8 \]

where \( x \) is the dog's age.

First, we can eliminate the fractions by multiplying the entire equation by 8 (the least common multiple of 4 and 8):

\[ 8 \left(\frac{x}{4}\right) + 8 \cdot 6 = 8 \left(\frac{x}{8}\right) + 8 \cdot 8 \]

This simplifies to:

\[ 2x + 48 = x + 64 \]

Now, we will move \( x \) to the left side and the constant terms to the right side:

\[ 2x - x = 64 - 48 \]

This simplifies to:

\[ x = 16 \]

So, the dog's age is \( 16 \) years old.

Therefore, the answer is:

16 years old.