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?
×
8
3
Number of Bananas Price
6 $3
16

6 · ? = 16

16 ÷ 6 =
6
16
​

Excellent!
Use the scale factor to find the price of 16 bananas. What number do you need to multiply $3 by to keep the ratio the same?
×
×
6
16
​

Number of Bananas Price
6 $3
16 as a fraction

Answer 1

To find the price of 16 bananas, we'll use the scale factor we calculated.

We have:

• The cost of 6 bananas is $3.
• We determined the scale factor is \( \frac{16}{6} = \frac{8}{3} \).

Now let's use the scale factor to determine the price for 16 bananas.

1. Determine the scale factor: \[ \text{Scale Factor} = \frac{8}{3} \]

2. Multiply the original price by the scale factor to find the price for 16 bananas: \[ \text{Price for 16 bananas} = \text{Price for 6 bananas} \times \text{Scale Factor} \] \[ = 3 \times \left(\frac{8}{3}\right) \]

3. Perform the multiplication:

   • When we multiply \(3\) by \(\frac{8}{3}\), the \(3\) in the numerator and denominator cancels out: \[ = \frac{3 \times 8}{3} = 8 \]

Thus, the cost of 16 bananas is $8.

Summary Table:

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

So, you can confidently state that 16 bananas cost $8.