Question

The lifespan of a guinea pig is 6 years less than that of a giraffe. The lifespan of a tiger is 4 times that of the guinea pig. If the total lifespan of the animals is 30 years, calculate the longevity for the giraffe.

Answer 1

Let's denote the lifespan of the giraffe as \( x \) years. According to the problem:

1. The lifespan of the guinea pig is \( x - 6 \) years.
2. The lifespan of the tiger is \( 4 \) times that of the guinea pig, which is \( 4(x - 6) \) years.

Now we can write an equation for the total lifespan of the three animals:

\[
x + (x - 6) + 4(x - 6) = 30
\]

Now let's simplify this equation step by step:

\[
x + (x - 6) + 4(x - 6) = 30
\]
\[
x + x - 6 + 4x - 24 = 30
\]
\[
(1 + 1 + 4)x - 30 = 30
\]
\[
6x - 30 = 30
\]
Add \( 30 \) to both sides:

\[
6x = 60
\]
Now, divide by 6:

\[
x = 10
\]

Thus, the lifespan of the giraffe is \( \boxed{10} \) years.

To verify:

- Lifespan of the giraffe: \( 10 \) years.
- Lifespan of the guinea pig: \( 10 - 6 = 4 \) years.
- Lifespan of the tiger: \( 4 \times 4 = 16 \) years.

Now, calculating the total lifespan:

\[
10 + 4 + 16 = 30
\]

The total is indeed \( 30 \) years, confirming that our solution is correct. The longevity for the giraffe is \( \boxed{10} \) years.