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Question

# A shopkeeper sells some television sets and A/C sets every day. He wants to earn a profit of at least Rs 10000 each week. For this, he must sell 20 television sets and 30 A/C sets every week or he must sell 50 television sets and 10A/C sets every week. Express this situation

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Solution

## Let the profit on each television set be Rs x and the profit on each A/C be Rs y. It is given that to earn a profit of at least Rs 6500, the shopkeeper should sell 20 television set and 30 A/C sets every week. Hence, the total profit earned by the shopkeeper by selling 20 television sets and 30 A/C sets is Rs (20x + 30y). Thus, 20x + 30y ≥ 10000 In either condition, it is given that to earn a profit of at least Rs 10000, the shopkeeper should sell 50 television sets and 10 A/C sets every week. Hence, the total profit earned by the shopkeeper by selling 50 television sets and 10 A/C sets is Rs (50x + 10y). Thus, 50x + 10y ≥ 10000. Hence, the given situation can be expressed mathematically by the following two inequalities: 20x + 30y ≥ 10000 and 50x + 10y ≥ 10000

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