Competition problem — Algebra — Olympiad Maths Prep

Library / /8 of 28

Algebra Difficulty 5.1 AIME, harder Find the answer Ukraine

There are discounts in the supermarket. An active customer will be given a discount of $4\%$ , if he buys goods for the sum of over $300$ ; and if the same customer buys goods for the sum of over $600$ , he will be given a discount of $10\%$ . What is the biggest amount of money that he can spend for goods if he has

a) $594$ ;
b) $534$ ?

Your answer

Solution

a) If a customer buys goods for the sum of $x \ge 600$ , he'll pay $10\%$ less the cost of these goods. Consequently, he can buy goods for the sum $x$ if $0.90x \le 594 \Rightarrow x \le 660$ at the most.

b) Analogously to the item a) we obtain that a customer will be given a discount of $4\%$ , to buy goods for the amount $x$ if $0.96x \le 534$ , that is $x \le 556.25$ .

Looking for a route rather than an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement and solution reproduced as published; topic and difficulty added by this site.