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

The Three Musketeers are off to adventures together but they like to pay their fair share of expenses. On a trip to England, each spends on meals an average of 78 ducats per week. Porthos eats 6 times as much as the average man, Athos eats 3 times less than Porthos and Aramis eats 5 times as much as the average man. What is the difference between the largest amount and the smallest amount one of them spends for food?

(characters from Alexandre Dumas - "The Three Musketeers")

If Aramis eats 3 times less than Porthos, this means he eats 2 times as much as the average man. Therefore, the amounts they eat are in the ratio: 6:2:5.

Denote these amounts by a, b, c. We have:

Applying the properties of equivalent ratios:

But:

Porthos pays 108 ducats.

Athos pays 36 ducats and Aramis pays 90 ducats.

The difference between the largest amount paid and the smallest amount paid is: