Question

В концертном зале 80 светильников: люстры и настенные бра. В каждой люстре 7 лампоч(-ек, -ки, -ка), в каждом бра - 3 лампочки. Число лампочек во всех люстрах равно числу лампочек во всех бра. Сколько люстр в зале?

Answer 1

Если все све­тиль­ни­ки — бра, то число лам­по­чек в них 80 · 3 = 240 , а в люст­рах — ноль. За­ме­ним одно бра одной люст­рой. Тогда число лам­по­чек в бра ста­нет 237, а в люст­рах — 7. Раз­ность числа лам­по­чек в люст­рах и в бра из­ме­нит­ся на 7 + 3 = 10. Чтобы лам­по­чек в бра и в люст­рах стало по­ров­ну, не­об­хо­ди­мо сде­лать 240 : 10 = 24 таких замен. Зна­чит, в зале 24 люстры.

Answer 2

#### Calculation of the Number of Chandeliers in the Concert Hall To determine the number of chandeliers in the concert hall, we need to consider the number of light bulbs in the chandeliers and wall sconces. Let's denote the number of light bulbs in each chandelier as "x" and the number of light bulbs in each wall sconce as "y". According to the given information, each chandelier has 7 light bulbs, and each wall sconce has 3 light bulbs. Additionally, the total number of light bulbs in all the chandeliers is equal to the total number of light bulbs in all the wall sconces. To find the number of chandeliers, we need to solve the equation: 7x = 3y Since the number of light bulbs in the chandeliers and wall sconces must be a whole number, we can find the common multiples of 7 and 3. The common multiples of 7 and 3 are: 21, 42, 63, 84, ... From the given information, we know that there are 80 light bulbs in total (in both the chandeliers and wall sconces). Therefore, we need to find a common multiple of 7 and 3 that is less than or equal to 80. By examining the common multiples, we can see that 21 is the largest common multiple that is less than or equal to 80. Let's substitute x = 21 and y = 7 into the equation: 7 * 21 = 3 * 7 147 = 21 Since the equation is true, we can conclude that there are **21 chandeliers** in the concert hall. #### Conclusion Based on the given information, there are 21 chandeliers in the concert hall.