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This problem trains for: SAT-I, AMC-8, GMAT, Math Kangaroo 3-4, Math Kangaroo 5-6.

If d dollars and q quarters buy Q quinces and D dates whereas q dollars and d quarters buy 5 more quinces and 5 less dates, what is the price difference between a quince and a date? Express the result in cents.

Denote the price of a quince with x and the price of a date with y.

Since the result is needed in cents we should express all the amounts in cents. Therefore each quarter is worth 25 cents and each dollar is worth 100 cents.

The first sentence can be written as:

equation

The second sentence is equivalent to:

equation

Subtract the first equation from the second one to get:

equation

equation

equation

equation

equation