To find out how many shoes Shira's Shoes sold in June, we start by using the information provided.
We know that 875,000 pairs of sandals represent 70% of the total number of shoes sold. We can set up the equation:
\[ 0.70 \times \text{Total Shoes} = 875,000 \]
To find the total number of shoes sold, we can rearrange this equation:
\[ \text{Total Shoes} = \frac{875,000}{0.70} \]
Now, calculating it:
\[ \text{Total Shoes} = 875,000 \div 0.70 = 1,250,000 \]
Thus, Shira's Shoes sold 1,250,000 pairs of shoes in June.
Now, let's analyze Emily's calculations. She wrote:
\[ \frac{part}{whole} = \frac{70 \times 8750}{100 \times 8750} = \frac{612,500}{875,000} \]
Analysis of Emily's Calculation:
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Error in Values: Emily calculated 70 times 8,750, which is incorrect in context. The correct calculation was to multiply \( 875,000 \) by the percentage \( 0.70 \) directly. The \( 8,750 \) in her calculation is incorrect and unnecessary; it appears she misunderstood the values involved.
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Understanding Percentages: Her method suggests she was trying to create a fraction to represent the part over the whole but ended up assigning arbitrary numbers rather than correctly using the known quantity of shoes sold.
Summary:
- Total shoes sold in June: 1,250,000 pairs
- Emily's mistake: She used incorrect values in her fraction and misinterpreted how to calculate the total based on the known 70% representation of the quantity sold. Instead of representing 70% as \(\frac{70}{100}\) concerning the total number of shoes, she used random values. Her fraction representation led to confusion and an incorrect conclusion.
This example illustrates the importance of accurately applying percentages in calculations.
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