Question

The Witches coven are making a potion and Ethel, Glinda, Locasta and Circe each add a different ingredient. When the potion is finished, there is 1/4 of the bat blood left, 1/3 of the knotgrass, 1/2 of the moonstone and 5/8 of the unicorn hair. Ethel used the most. Glinda used the least. Locasta used more than Circe. Who used the moonstone?

Answer 1

Circe. Given that the four witches each added a different ingredient and since the absolute amount of each ingredient isn't mentioned, I will assume that "most", "least" and other comparisons are referring to fractions. So first, let's order the ingredients from least to most in terms of fractions. The easiest way to compare them is to calculate the least common denominator for the 4 fractions involved and convert all the fractions to use that common denominator. For 4 and 3, the LCD is 12. And 12 works ok for 2, but it won't work for 8. The LCD for 12 and 8 is 24 and that will work for all of the fractions. Bat Blood 1/4 - 6/24 Knotgrass 1/3 - 8/24 Moonstone 1/2 - 12/24 Unicorn Hair 5/8 - 15/24 So we now have the ingredients properly sorted by how much is left over, so the most used will be the 1st in the list and the least used will be the last. Now let's look at who used what. "Ethel used the most." Which would mean that Ethel used the Bat Blood. "Glinda used the least" Which would mean that Glinda used the Unicorn hair. "Locasta used more than Circe" Circe hasn't been mentioned yet, but there's only 2 ingredients that haven't been claimed. So it's safe to say that Locasta used the most used of the two ingredients unclaimed. And that would be Knotgrass. So the final question is "Who used the moonstone?" and there's only 1 witch that hasn't been assigned an ingredient. And that witch is Circe. So Circe used the moonstone.

Answer 2

The moonstone was used by $\fbox{\begin\\\ \bf Circe\\\end{minispace}}$.

Further explanation:

It is given that a potion is prepared by a group of witches. The members in the group are Ethel, Glinda, Locasata and Circe.

The ingredients used in the preparation of the potion are bat blood, knotgrass, moonstone and unicorn hair.

Each member of the group add a different ingredient which means that no two member of the group add the same ingredient.

As the preparation of the potion is finished it is observed that the $\dfrac{1}{4}th$ of the bat blood is left, $\dfrac{1}{3}rd$ of the knotgrass is left, $\dfrac{1}{2}nd$ of the moonstone is left and $\dfrac{5}{8}th$ of the unicorn hair is left.

From the above statement it is concluded that $25\%$ of the bat blood is left, $33.33\%$ of the knotgrass is left, $50\%$of the moonstone is left and $62.5\%$ of unicorn hair is left.

Therefore, the percentage of ingredients used in the preparation of the potion are as follows:

Bat blood: $75\%$ is used

Knotgrass: $66.67\%$ is used

Moonstone: $50\%$ is used

Unicorn hair: $37.5\%$ is used

As per the question Ethel used the most so, the ingredient bat blood was used by Ethel.

As per the question Glinda used the least so, the ingredient unicorn hair was used by Glinda.

It is given that Locasta used more than Circe so, the ingredient knotgrass was used by Locasta and moonstone was used by Circe.

Therefore, the ingredient moonstone was used by $\fbos{\begin\\\ \bf Circe\\\end{minispace}}$.

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Percentages and Fraction

Keywords: Percentages, fraction, Ethel, Glinda, Locasata, Circe, potion, bat blood, knotgrass, moonstone, unicorn hair, numbers, witches, coven, simplification.