2. Use a ratio box to solve this problem. Adriana's soccer ball is covered with a pattern of pentagons and hexagons in the ratio of 3 to 5 . If there are 12 pentagons, how many hexagons are in the pattern?

Question

UpStudy AI · Accepted Answer

$$
\textbf{Step 1: Write the ratio of pentagons to hexagons.}
$$

The ratio given is $$ 3:5 $$, meaning that for every $$ 3 $$ pentagons there are $$ 5 $$ hexagons.

$$
\textbf{Step 2: Set up the ratio box.}
$$

$$
\begin{array}{|c|c|}
\hline
\textbf{Pentagons} & \textbf{Hexagons} \
\hline
3 & 5 \
\hline
12 & x \
\hline
\end{array}
$$

$$
\textbf{Step 3: Set up a proportion to solve for } x.
$$

Since the ratios must be equal, we have:

$$
\frac{3}{5} = \frac{12}{x}
$$

$$
\textbf{Step 4: Solve the proportion.}
$$

Cross-multiply:

$$
3x = 5 \times 12
$$

$$
3x = 60
$$

Divide by $$ 3 $$:

$$
x = \frac{60}{3} = 20
$$

$$
\textbf{Answer:} \quad 20 \text{ hexagons.}
$$
There are 20 hexagons in the pattern.

Use a ratio box to solve this problem. Adriana’s soccer ball is covered
with a pattern of pentagons and hexagons in the ratio of 3 to 5 . If there
are 12 pentagons, how many hexagons are in the pattern?

Upstudy AI Solution

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Use a ratio box to solve this problem. Adriana’s soccer ball is covered with a pattern of pentagons and hexagons in the ratio of 3 to 5 . If there are 12 pentagons, how many hexagons are in the pattern?