To find the price of 12 pears at the same rate, we need to follow the steps we've established.
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Set Up the Table:
| Number of Pears | Price | |------------------|-------| | 8 | $2 | | 12 | $? |
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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 \( 12 \div 8 \):
\[ \frac{12}{8} = \frac{3}{2} \text{ or } 1.5 \]
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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 \( \frac{3}{2} \):
\[ 2 \cdot \frac{3}{2} \]
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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 |