To find the total number of shoes sold by Shira's Shoes in June, we can set up the problem based on the information provided. Given that 875,000 pairs of sandals represent 70% of the total shoes sold, we can use the following equation:
Let \( x \) be the total number of shoes sold.
We know that: \[ 0.70x = 875,000 \]
To find \( x \), divide both sides by 0.70: \[ x = \frac{875,000}{0.70} \] Calculating: \[ x = 1,250,000 \]
Thus, the total number of shoes sold by Shira’s Shoes in June was 1,250,000 pairs.
Analyzing Emily's Calculations
Emily's calculations attempted to express the relationship between the part and whole in a different way. Let's analyze what she did:
She wrote: \[ \frac{part}{whole} = \frac{70 \times 8,750}{100 \times 8,750} \]
This expression does not correctly reflect the problem because:
- \(8,750\) is not a coherent value in this context. It seems Emily may have misunderstood the percentage representation. The part should be \(875,000\) (the number of sandals sold) while the whole should be the total shoes sold.
- The calculations should keep the original figures unchanged. Using \(8,750\) introduces confusion, as it doesn't relate to the numbers in the problem.
Conclusion
Emily made an error in substituting \(8,750\) into her calculations. The correct formulation should be \( \frac{875,000}{total\ shoes\ sold} = \frac{70}{100} \) instead of her method. The total number of shoes sold in June should be correctly established as 1,250,000 pairs.
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