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 =
as a fraction

Answer 1

To find the scale factor, we can divide 16 by 6:

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

We can simplify \(\frac{16}{6}\) by finding the greatest common divisor of 16 and 6. Both can be divided by 2:

\[ \frac{16 \div 2}{6 \div 2} = \frac{8}{3} \]

So, the scale factor is \(\frac{8}{3}\).

Now, we can use this scale factor to find the price of 16 bananas. Since we know the price of 6 bananas is $3, we can set up the following multiplication equation to find the price of 16 bananas:

\[ \text{Price of 16 bananas} = \text{Price of 6 bananas} \times \text{Scale factor} \]

Substituting the values gives us:

\[ \text{Price of 16 bananas} = 3 \times \frac{8}{3} \]

The \(3\) in the numerator and denominator cancels out:

\[ \text{Price of 16 bananas} = 8 \]

Thus, the cost of 16 bananas at this rate will be $8.

Here’s how the table would look:

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