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



=
·
·

1 answer

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 |