91Ó°ÊÓ

An integer solution means the result of a calculation must be a whole number, with no fractions or decimals involved. In our exercise, both \( p \) and \( q \) are specified as integers. Thus, when we compute \( p \) from \( p = 1.15q \), the end result, \( p \), has to remain an integer.

To make \( 1.15q \) an integer, \( q \) must be a number that, when multiplied by 1.15, gives a whole number. This idea is critical since any fractional result for \( p \) would not satisfy the given condition in the problem.

In this context, rewriting 1.15 as \( \frac{23}{20} \) helps us understand that \( q \) needs to be a multiple of 20, ensuring \( \frac{23}{20}q \) results in an integer.

• This simplifies the understanding of how integer constraints affect our solution.
• It ensures we look for values of \( q \) such that \( p \) remains a whole number.

Fractions and ratios are key to understanding the relationship between two numbers. In the problem, we convert the decimal 1.15 into a fraction for easier manipulation, \( \frac{23}{20} \). This fraction indicates how \( p \) relates to \( q \).

Fractions, like \( \frac{23}{20} \), show us how one quantity is multiplied to obtain another. Here, \( 23 \) is the numerator and \( 20 \) is the denominator, indicating that \( p \) is 23 parts of 20 parts of \( q \).

• This transformation of the decimal helps us apply the concept of ratios, showing a clear multiplicative relationship.
• Understanding how decimals convert to fractions assists in precise calculations and ensures integer results, aligning with the integer condition in the problem.

Breaking down a problem into manageable steps is crucial for finding the right solution. In this problem, we use a structured approach:

**Step 1: Rewriting the Equation**
Start by expressing the given decimal, 1.15, as a fraction. This sets the foundation for further calculations and understanding the nature of \( p \) and \( q \).

**Step 2: Checking Integer Solutions**
Once expressed as \( p = \frac{23}{20}q \), we focus on finding values of \( q \) that keep \( p \) as an integer. Discovering that \( q \) must be a multiple of 20 is vital.

**Step 3: Substituting Values**
Testing the given options, we solve to find which values match \( \frac{23}{20}q \). This helps us identify the potential solution that satisfies the integer condition.

By verifying option \( E \), \( p = 23 \), we ensure it conforms to all derived equations. This systematic method guarantees accurate and logical solution finding, crucial for problems involving integer constraints and ratios.