Question

Solve the riddle.

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.**