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This problem trains for: SAT-I, CAHSEE, AMC-8, Math Kangaroo 5-6, Math Kangaroo 7-8.

When Jacob Blivens, the famous 'good little boy' decided to make good on his promise to learn the whole periodic table of elements, he learned 20% of it in the first day, 30% of the remaining in the second day, 20 elements in the third day. For the fourth day, he had 10% more elements to learn than in the third day, when the neighbor's cat got irritated by the table and clawed it to shreds. Poor Jacob's plan failed pitifully. How many chemical elements were known in the time of Mark Twain?

(character from Mark Twain's "The Story of the Good Little Boy")

This problem is easily solved by backtracking.

If he memorized 20 elements on the third day, on the fourth day he must have memorized:

equation

for a total over the last two days of 42 elements.

In the first day he memorized 20% of the total number of elements.

In the second day he memorized 30% of the 80%, remaining, which is equivalent to 24% of the total:

equation

This means that in the first two days he memorized 44% of the total. The last two days represent 56% of the total number of elements:

equation

equation

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In the times of Mark Twain only about 75 chemical elements were known.