To compare how much each person paid, we first need to express their payments in the same format. We can do this by converting the fractions and percentages to a common denominator.
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Kim paid: \( \frac{3}{7} \) of the bill.
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Sherri paid: \( 35% \) of the bill can be expressed as a fraction: \[ 35% = \frac{35}{100} = \frac{7}{20}. \]
Now we need to compare \( \frac{3}{7} \) and \( \frac{7}{20} \). To do this, we can find a common denominator. The least common multiple of 7 and 20 is 140.
Convert Kim's payment: \[ \frac{3}{7} = \frac{3 \times 20}{7 \times 20} = \frac{60}{140}. \]
Convert Sherri's payment: \[ \frac{7}{20} = \frac{7 \times 7}{20 \times 7} = \frac{49}{140}. \]
Now we compare the two payments:
- Kim: \( \frac{60}{140} \)
- Sherri: \( \frac{49}{140} \)
Since \( \frac{60}{140} > \frac{49}{140} \), Kim paid more than Sherri.
Now let's find out how much Judy paid. The total bill can be represented as 1 (or \( \frac{140}{140} \) in terms of the common denominator). The amount paid by Judy is: \[ 1 - \left( \frac{3}{7} + \frac{7}{20} \right) = 1 - \left( \frac{60}{140} + \frac{49}{140} \right) = 1 - \frac{109}{140} = \frac{140}{140} - \frac{109}{140} = \frac{31}{140}. \]
Now we compare:
- Kim paid \( \frac{60}{140} \).
- Sherri paid \( \frac{49}{140} \).
- Judy paid \( \frac{31}{140} \).
Thus, the ranking in terms of who paid the most is:
- Kim: \( \frac{60}{140} \)
- Sherri: \( \frac{49}{140} \)
- Judy: \( \frac{31}{140} \)
So, the true statement is: Kim paid the most.