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.

Question

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.