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?
×
8
3
×
6
16
​

Number of Bananas Price
6 $3
16
Excellent!
To find the price of 16 bananas, you can multiply $3 by the scale factor,
6
16
​
. Write 3 ·
6
16
​
as a single fraction.
×
6
16
​

×
6
16
​

Number of Bananas Price
6 $3
16

3 ·
6
16
​


=
3
·
16
1
·
6
Great job!
To help you find the price of 16 bananas, find
1
3
​
·
6
16
​
. Select all the equivalent values for
1
3
​
·
6
16
​
.
×
6
16
​

×
6
16
​

Number of Bananas Price
6 $3
16 ?

3 ·
6
16
​


=
3 · 16
1 · 6

48

8

6
48
​


6
16
​

Answer 1

Let's break down the solution to find the cost of 16 bananas using the scale factor derived from the cost of 6 bananas.

Cost Calculation Setup

1. Initial Information:

   • Cost for 6 bananas: $3
   • Target number of bananas: 16

2. Establish a Table: | Number of Bananas | Price | |--------------------|--------| | 6 | $3 | | 16 | ? |

3. Identify Scale Factor:

   • We set up the relationship: \[ 6 \cdot ? = 16 \]
   • To find the scale factor, rewrite it in division form: \[ ? = \frac{16}{6} \]

4. Calculate the Scale Factor:

   • Calculate \( \frac{16}{6} \): \[ \frac{16}{6} = \frac{8}{3} \quad (\text{simplified}) \]
   • Now the scale factor is \( \frac{8}{3} \).

Price Calculation for 16 Bananas

5. Price of 16 Bananas:
   • To find the price of 16 bananas, multiply the original cost by the scale factor: \[ \text{Price for 16 bananas} = 3 \cdot \frac{8}{3} \]
   • The calculation simplifies as follows: \[ 3 \cdot \frac{8}{3} = \frac{3 \cdot 8}{3} = 8 \]

Final Results

6. Final Table: | Number of Bananas | Price | |--------------------|--------| | 6 | $3 | | 16 | $8 |

Answer: The cost of 16 bananas is $8.

Equivalent Value Evaluation

Now, let's identify the equivalent values for \( \frac{3 \cdot 16}{1 \cdot 6} \):

1. Calculation: \[ \frac{3 \cdot 16}{1 \cdot 6} = \frac{48}{6} = 8 \]

2. Equivalent values are:

   • 48 (numerator in original form)
   • 8 (final simplified form)
   • 6 (denominator from the original fraction)
   • \( \frac{8}{3} \) (scale factor)

So, the valid selections based on your question would be 8, 48, and \( \frac{8}{3} \).

If you need clarification or further assistance, feel free to ask!