what is the minimum number of Paver 3 stones Laila needs to buy if she decides to use Paver 3 for her driveway, given that she needs twice as many Paver 1 stones as Paver 2 stones and half as many Paver 1 stones as Paver 3 stones?

Answer 1

To determine the minimum number of Paver 3 stones Laila needs to buy, let's define the number of stones she needs for each type:

Let:

• \( x \) = number of Paver 2 stones
• \( y \) = number of Paver 1 stones
• \( z \) = number of Paver 3 stones

From the problem, we know:

1. Laila needs twice as many Paver 1 stones as Paver 2 stones: \[ y = 2x \]

2. She needs half as many Paver 1 stones as Paver 3 stones: \[ y = \frac{1}{2}z \quad \text{or equivalently, } z = 2y \]

We want to express everything in terms of \( x \).

First, substitute \( y = 2x \) into \( z = 2y \):

\[ z = 2(2x) = 4x \]

Now we have all the variables expressed in terms of \( x \):

• \( y = 2x \)
• \( z = 4x \)

To find the minimum number of Paver 3 stones \( z \), we simply need \( x \) to be a positive integer. As \( x \) is the number of Paver 2 stones, the smallest possible value for \( x \) is 1.

Thus, substituting \( x = 1 \):

\[ z = 4 \cdot 1 = 4 \]

Therefore, the minimum number of Paver 3 stones Laila needs to buy is:

\[ \boxed{4} \]