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


· =

Answer 1

To find the cost of 12 pears using the scale factor based on the cost of 8 pears, we can first determine the scale factor between the two quantities of pears.

1. **Set up the relationship**: We want to find the price for 12 pears based on the price for 8 pears.

2. **Find the scale factor**:
- The number of pears increases from 8 to 12.
- To find the scale factor, we can set up the following equation:
\[
\text{Scale Factor} = \frac{\text{Number of Pears (new)}}{\text{Number of Pears (original)}} = \frac{12}{8} = 1.5
\]

3. **Write the multiplication equation**:
- Since the scale factor is 1.5, you can multiply the original price by this scale factor to get the new price.
\[
2 \, (\text{original price}) \times 1.5 = \text{new price}
\]

4. **Calculate the new price**:
\[
2 \times 1.5 = 3
\]

So, the price of 12 pears is $3.

5. **Set up the table**:

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

Thus, the cost of 12 pears at this rate would be $3.