Question

trent is making centerpieces for the school’s valentine’s day dance. he divides a bucket of roses evenly among 18 centerpieces. each centerpiece gets 6 roses. let ( r ) represent how many roses were in the bucket. which equation models the problem? (\frac{r}{6} = 18) (6r = 18) solve this equation to find how many roses were in the bucket. (\boxed{quad}) roses

Explanation:

Part 1: Identify the Correct Equation

We know that the total number of roses \( r \) is divided evenly among 18 centerpieces, and each centerpiece gets 6 roses. So the relationship is \( \frac{r}{18}=6 \) (wait, no, wait—wait, the problem says "divides a bucket of roses evenly among 18 centerpieces. Each centerpiece gets 6 roses." So total roses \( r \) divided by 18 centerpieces equals 6 roses per centerpiece. So the equation should be \( \frac{r}{18} = 6 \)? Wait, no, the options given are \( \frac{r}{6}=18 \) and \( 6r = 18 \). Wait, let's re-express: If there are 18 centerpieces, each with 6 roses, then total roses \( r=18\times6 \). So rearranged, \( \frac{r}{6}=18 \), because \( r = 18\times6 \) implies \( \frac{r}{6}=18 \). So the correct equation is \( \frac{r}{6}=18 \).

Step 1: Multiply both sides by 6

To solve \( \frac{r}{6}=18 \), we multiply both sides of the equation by 6 to isolate \( r \).
\( \frac{r}{6} \times 6 = 18 \times 6 \)

Step 2: Simplify both sides

Simplifying the left side, \( \frac{r}{6} \times 6 = r \). Simplifying the right side, \( 18 \times 6 = 108 \). So we get \( r = 108 \).

Answer:

\(\frac{r}{6} = 18\)

Part 2: Solve the Equation