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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

Robin Hood and his Merry Men robbed the Sheriff of Nottingham of a round sum silver pennies. Friar Tuck divided the sum into three parts: one for the poor, one for the Merry Men's treasury and one for hiding where archaeologists might find it one day. First, he divided the loot into parts proportional to the numbers 30, 40, 17, then Robin said the archaeologists were getting too much and changed the numbers to 30, 40, 13. In the second case, the archaeologists' pile is smaller by 280 pennies. What was the total amount of silver pennies?

(characters from Sir Walter Scott's "Ivanhoe")

The amounts for the first case are of the form:

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The amounts for the second case are of the form:

equation

We know that:

equation

Therefore:

equation

equation

equation

equation

equation

The total amount is the same in both cases:

equation

equation

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and the total amount is:

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