We are given the equation:

\[
a \cdot (n + y) = 10y + 32
\]

To solve this equation, we can start by distributing \( a \) on the left-hand side:

\[
a \cdot n + a \cdot y = 10y + 32
\]

This simplifies to:

\[
an + ay = 10y + 32
\]

Now, we want to isolate \( a \). First, let's move all the terms involving \( y \) to one side:

\[
an = 10y - ay + 32
\]

Factor out \( y \) from the terms on the right-hand side:

\[
an = y(10 - a) + 32
\]

Now, we have an equation with \( a \), \( n \), \( y \), and constants. To further simplify, we need additional information about \( n \) and \( y \) (or one of the variables) to solve for \( a \).

Would you like to provide specific values for \( n \) or \( y \), or would you prefer to keep the equation in its general form? Feel free to ask for clarification.

Here are 5 related questions to consider:

1. What are the values of \( n \) and \( y \), if known?
2. Do you want to solve for \( a \) in terms of \( n \) and \( y \)?
3. Would you like to explore this problem graphically?
4. What would change in the equation if we know that \( y = 2 \) or \( n = 5 \)?
5. Can the problem be expanded to a system of equations?

**Tip

Understand how to solve the linear equation a(n + y) = 10y + 32 using the distributive property and algebraic manipulation. This problem involves isolating variables and simplifying expressions. Suitable for students in Grades 8-10.

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