Question

A grocery store sells pears, where 8 pears cost $2. How much will 12 pears cost at this rate? Use the scale factor to help you solve.
Start by setting up a table that could be used to find the price of 12 pears.
Number of Pears Price

8
$
2

12
$
?
Good work!
One way to find the cost of 12 pears is to use the scale factor. Write a multiplication equation you could use to find the scale factor.
× ?
Number of Pears Price
8 $2
12



8
·
?
=
12
Great job!
To help you find the scale factor, rewrite the multiplication equation as a division equation.
× ?
Number of Pears Price
8 $2
12

8 · ? = 12


12
÷
8
= ?
Great job!
To find the scale factor, we can divide. What is 12 divided by 8?
× ?
Number of Pears Price
8 $2
12

8 · ? = 12

12 ÷ 8 =
12
8
Great job!
What is the scale factor?
×
3
2
Number of Pears Price
8 $2
12

8 · ? = 12

12 ÷ 8 =
8
12
​

Great job!
Use the scale factor to find the price of 12 pears. What number do you need to multiply $2 by to keep the ratio the same?
×
12
8
×
8
12
​

Number of Pears Price
8 $2
12
Nice!
To find the price of 12 pears, you can multiply $2 by the scale factor,
8
12
​
. Write 2 ·
8
12
​
as a single fraction.
×
8
12
​

×
8
12
​

Number of Pears Price
8 $2
12


2 ·
8
12
​


=
·
·

Answer 1

To find the price of 12 pears at the same rate, we need to follow the steps we've established.

1. **Set Up the Table:**

| Number of Pears | Price |
|------------------|-------|
| 8 | $2 |
| 12 | $? |

2. **Finding the Scale Factor:**

We already established the multiplication equation to find the scale factor:

\( 8 \cdot ? = 12 \)

To find the scale factor, we rewrite the equation as:

\( 12 \div 8 = ? \)

Now we calculate \( 12 \div 8 \):

\[
\frac{12}{8} = \frac{3}{2} \text{ or } 1.5
\]

3. **Using the Scale Factor:**

The scale factor is \( \frac{3}{2} \). To find the price of 12 pears, we multiply the price for 8 pears by the scale factor. So we need to multiply $2 by \( \frac{3}{2} \):

\[
2 \cdot \frac{3}{2}
\]

4. **Writing It as a Single Fraction:**

We write the multiplication:

\[
2 \cdot \frac{3}{2} = \frac{2 \cdot 3}{2} = \frac{6}{2} = 3
\]

So, the cost of 12 pears will be $3.

Finally, we can update the table:

| Number of Pears | Price |
|------------------|-------|
| 8 | $2 |
| 12 | $3 |