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

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?
×
Number of Pears Price
8 $2
12

8 · ? = 12

12 ÷ 8 =
8
12
​
as a fraction

Answer 1

To find the scale factor, we divide 12 by 8:

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

Therefore, the scale factor is \( \frac{3}{2} \), or 1.5, meaning that the number of pears increases by 1.5 times.

Now, to find the cost of 12 pears, we can multiply the cost of 8 pears by the scale factor:

1. The cost of 8 pears is $2.
2. The cost of 12 pears will be:

\[ 2 \times 1.5 = 3 \]

So, the price for 12 pears at this rate will be $3.

Here is how the table looks after including our calculations:

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