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
$
?
Great job!
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
You got it!
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
= ?
Excellent!
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 =

Answer 1

To find the scale factor, let's compute \( 16 \div 6 \):

\[ 16 \div 6 = \frac{16}{6} = \frac{8}{3} \approx 2.67 \]

Now, we can interpret this in relation to the price. For every 6 bananas that cost $3, we need to multiply the cost by the scale factor to find the price for 16 bananas.

Next, since the scale factor is \( \frac{8}{3} \), we will use this to find the price of 16 bananas:

1. Find the cost for 1 banana:

\[ \text{Cost per banana} = \frac{3}{6} = 0.50 \text{ dollars per banana} \]

2. Now multiply the cost of one banana by 16:

\[ \text{Cost for 16 bananas} = 0.50 \times 16 = 8 \]

Thus, the cost for 16 bananas is $8.

Let’s complete the table:

| Number of Bananas | Price | |-------------------|-------| | 6 | $3 | | 16 | $8 |

So to recap:

• The scale factor for the number of bananas is \( \frac{8}{3} \).
• The price for 16 bananas is $8.