Question

A grocery store sells bananas, where 6 bananas cost $3. How much will 16 bananas cost at this rate? Use the scale factor to help you solve.
Start by setting up a table that could be used to find the price of 16 bananas.
Number of Bananas Price

6
$
3

16
$
?
Good work!
One way to find the cost of 16 bananas is to use the scale factor. Write a multiplication equation you could use to find the scale factor.
× ?
Number of Bananas Price
6 $3
16



6
·
?
=
16
Good work!
To help you find the scale factor, rewrite the multiplication equation as a division equation.
× ?
Number of Bananas Price
6 $3
16

6 · ? = 16


16
÷
6
= ?
Nice!
To find the scale factor, we can divide. What is 16 divided by 6?
× ?
Number of Bananas Price
6 $3
16

6 · ? = 16

16 ÷ 6 =
8
3
You got it!
What is the scale factor?
×
Number of Bananas Price
6 $3
16

6 · ? = 16

16 ÷ 6 =
6
16
​
as a fraction

Answer 1

To find the cost for 16 bananas, let's go through the problem step-by-step using the information already provided.

1. **Price of Bananas**: We know that 6 bananas cost $3.
2. **Set up a table**:

| Number of Bananas | Price |
|-------------------|----------|
| 6 | $3 |
| 16 | ? |

3. **Find the scale factor**: We need to determine how many times larger 16 bananas is compared to 6 bananas. We set up the multiplication equation as:

\[
6 \cdot ? = 16
\]

4. **Convert to division**:

\[
? = \frac{16}{6}
\]

5. **Perform the division**:

\[
16 \div 6 = \frac{16}{6} = \frac{8}{3}
\]

6. **Scale factor**: The scale factor is \( \frac{8}{3} \).

Now, since we have the scale factor, we can find the price for 16 bananas. The cost of 6 bananas is $3. To find the cost for 16 bananas, we multiply the price of 6 bananas by the scale factor:

\[
\text{Price for 16 bananas} = 3 \cdot \frac{8}{3}
\]

The \( 3 \)s cancel out:

\[
= 8
\]

So, the cost for 16 bananas will be **$8**.

To summarize:
- The scale factor is \( \frac{8}{3} \).
- The price for 16 bananas is **$8**.