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.

Question

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.