Questions: Mia wrote the expression 8(r+4)+9 to show how much money 8 friends paid for tickets to the movies. Which expression is equivalent to the one Mia wrote?

Mia wrote the expression 8(r+4)+9 to show how much money 8 friends paid for tickets to the movies. Which expression is equivalent to the one Mia wrote?

Transcript text: 1. Mia wrote the expression $8(r+4)+9$ to show how much money 8 friends paid for tickets to the movies. Which expression is equivalent to the one Mia wrote?

Solution

Solution Steps

To find an equivalent expression to the one Mia wrote, we need to apply the distributive property to the expression $8(r+4)+9$. The distributive property states that $a(b+c) = ab + ac$. We will distribute the 8 across the terms inside the parentheses and then simplify the expression.

Step 1: Distribute the Expression

We start with the expression $8(r + 4) + 9$. To simplify this, we apply the distributive property:

\[ 8(r + 4) = 8r + 32 \]

Step 2: Combine Like Terms

Next, we add the constant term from the original expression:

\[ 8r + 32 + 9 = 8r + 41 \]