We are given that Lily has pineapples and apples in a ratio of 128:60. We need to determine how many pineapples she has if she has 15 apples.

Step-by-Step Solution:

1. The ratio of pineapples to apples is given as $\frac{128}{60}$.

2. Set up the ratio to find the number of pineapples, denoted as $x$, when there are 15 apples:

   $\frac{128}{60} = \frac{x}{15}$

3. To solve for $x$, cross-multiply:

   $128 \times 15 = 60 \times x$

   Simplifying the left-hand side:

   $1920 = 60x$

4. Now, divide both sides by 60 to solve for $x$:

   $x = \frac{1920}{60} = 32$

Thus, Lily has 32 pineapples if she has 15 apples.

Would you like further details or have any other questions?

Relative questions:

1. What is the general method for solving ratio problems?
2. How do you simplify a ratio like 128:60?
3. How do you know when to multiply or divide when solving ratio problems?
4. Can ratios be used in other contexts besides fruit?
5. How would the result change if the number of apples was doubled?

Tip:

When working with ratios, it helps to simplify them first to make calculations easier. For example, $128:60$ can be simplified by dividing both terms by their greatest common divisor (GCD).