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 =
as a fraction

1 answer

To find the scale factor for the number of pears, we perform the division:

\[ 12 \div 8 = \frac{12}{8} \]

This fraction can be simplified:

\[ \frac{12}{8} = \frac{3}{2} \text{ (by dividing both the numerator and the denominator by 4)} \]

So, \( 12 \div 8 = \frac{3}{2} \).

Now that we have the scale factor of \(\frac{3}{2}\), we can use it to find the price of 12 pears. The price of 8 pears is $2.

To find the price for 12 pears, we multiply the price of 8 pears by the scale factor:

\[ \text{Price for 12 pears} = 2 \times \frac{3}{2} \]

Now we multiply:

\[ \text{Price for 12 pears} = 2 \times \frac{3}{2} = 3 \]

Thus, the price for 12 pears will be $3.

To summarize, here’s the completed table with the price:

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