Plugging In: Invisible Plugging In - Fractions
In a bakery shop $$\frac{3}{7}$$ of the muffins are oatmeal, and $$\frac{3}{5}$$ of the remaining muffins are cranberry muffins. Of the muffins that are neither oatmeal nor cranberries, $$\frac{1}{2}$$ are plain chocolate muffins. What fraction of all the muffins are neither oatmeal, cranberries, nor plain chocolate?
Correct.
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Assume that there are 70 muffins in the bakery shop.
Model the problem using a tree:
Of the total muffins, $$\frac{3}{7}$$ of them are oatmeal, so there are
>$$\frac{3}{7}\times 70 = 3 \times 10 = 30 $$ oatmeal muffins.
Of the remaining 40 muffins, $$\frac{3}{5}$$ are cranberries, so there are
>$$\frac{3}{5}\times 40 = 3\times 8 = 24$$ cranberry muffins.
Of the remaining $$40-24=16$$ muffins, half are plain chocolate. So there are 8 plain chocolate muffins with 8 more remaining muffins that are not members of either of the categories we've dealt with so far.
That means that the fraction of muffins that are not oatmeal, cranberry, or plain chocolate is $$\frac{8}{70}$$. Reduce that fraction by 2 to get $$\frac{4}{35}$$.
Of the total muffins, $$\frac{3}{7}$$ of them are oatmeal, so there are
>$$\frac{3}{7}\times 70 = 3 \times 10 = 30 $$ oatmeal muffins.
Of the remaining 40 muffins, $$\frac{3}{5}$$ are cranberries, so there are
>$$\frac{3}{5}\times 40 = 3\times 8 = 24$$ cranberry muffins.
Of the remaining $$40-24=16$$ muffins, half are plain chocolate. So there are 8 plain chocolate muffins with 8 more remaining muffins that are not members of either of the categories we've dealt with so far.
That means that the fraction of muffins that are not oatmeal, cranberry, or plain chocolate is $$\frac{8}{70}$$. Reduce that fraction by 2 to get $$\frac{4}{35}$$.
Incorrect.
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Incorrect.
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Incorrect.
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This is the fraction of muffins that *are* oatmeal, cranberries, or plain chocolate. But what did the question ask?
Incorrect.
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$$\frac{1}{70}$$
$$\frac{4}{35}$$
$$\frac{18}{70}$$
$$\frac{52}{70}$$
$$\frac{31}{35}$$
