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

÷ = ?

1 answer

To find the scale factor for the number of pears, we can rewrite the multiplication equation \(8 \cdot ? = 12\) as a division equation.

Setting up the division equation:

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

Now we simplify the fraction:

\[ ? = \frac{12 \div 4}{8 \div 4} = \frac{3}{2} = 1.5 \]

So the scale factor is \(1.5\). This means that the number of pears is increasing by a factor of \(1.5\).

Now, we can use this scale factor to find the cost of 12 pears. Since the cost of 8 pears is $2, we can multiply this by the scale factor to find the price for 12 pears:

Finding the cost of 12 pears:

\[ \text{Cost of 12 pears} = 2 \cdot 1.5 \] \[ = 3 \]

Thus, the cost of 12 pears will be $3.

Final table:

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