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Print49th Mathematical Olympiad in Ukraine
Ukraine algebra
Problem
There are discounts in the supermarket. An active customer will be given a discount of , if he buys goods for the sum of over ; and if the same customer buys goods for the sum of over , he will be given a discount of . What is the biggest amount of money that he can spend for goods if he has
a) ; b) ?
a) ; b) ?
Solution
a) If a customer buys goods for the sum of , he'll pay less the cost of these goods. Consequently, he can buy goods for the sum if at the most.
b) Analogously to the item a) we obtain that a customer will be given a discount of , to buy goods for the amount if , that is .
b) Analogously to the item a) we obtain that a customer will be given a discount of , to buy goods for the amount if , that is .
Final answer
a) 660; b) 556.25
Techniques
Linear and quadratic inequalitiesDecimals