Plugging In: Invisible Plugging In - Fractions
Gordon sold one-third of his baseball cards on Monday. He sold one-third of the remaining cards on Tuesday. Of the remainder, he sold one-fourth on Wednesday and one-fifth on Thursday. What fraction of Gordon's cards remains unsold?
Incorrect.
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Incorrect.
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Correct.
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The invisible variable is Gordon's number of cards. To find a good number to __Plug In__ a good, multiply the bottoms of the fractions in the problem
>$$3\times 3\times 4\times 5=180$$
Based on this, Gordon sold $$\frac{1}{3}\cdot 180=60$$ on Monday. Of the remainder, 120, he sold $$\frac{1}{3}$$ on Tuesday (40).
Here comes the trick—in the next two days, he sells one-fourth and
one-fifth, but here both fractions are taken out of 80 and not from
successively smaller numbers since both are taken out of the number of cards remaining on Wednesday. There's no "out of the remaining" for Thursday.
Thus, of the remaining 80, he sold $$\frac{1}{4}$$ on Wednesday (20) and $$\frac{1}{5}$$ on Thursday (16), leaving 44 unsold cards. Thus, the fraction of unsold cards is $$\frac{44}{180}$$, or $$\frac{11}{45}$$.
*Note that in the third sentence of the question stem, the "one-fourth" and "one-fifth" both apply to the amount of cards after Tuesday. You may have been tricked by not reading and thinking that Thursday worked the same way as Tuesday and Wednesday.*
Incorrect.
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Incorrect.
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$$\frac{4}{45}$$
$$\frac{5}{45}$$
$$\frac{11}{45}$$
$$\frac{2}{9}$$
$$\frac{1}{3}$$
