Question

Аня посадила вдоль дорожки некоторое количество луковиц лилий. Потом пришел Боря и между каждой парой соседних посаженных луковиц посадил новую луковицу. Потом пришла Вика и между каждой парой соседних луковиц, посаженных до нее, посадила новую луковицу. Потом пришел Гоша и сделал то же самое. Все посаженные луковицы взошли и расцвело 129 лилий. Сколько луковиц посадила Аня?

Answer 1

Решение:
Костя посадил X
ТаняX-1
Инна Х+Х-1-1=2 Х-2
Дима Х+Х-1+2 Х-1=1Х-1
Всего Х+Х-1+2Х-2+4Х-4=113
8Х-7=113
8Х=120
Х=120:8
Х=15
Ответ 15 луковиц

Answer 2

Problem Analysis

Аня initially planted a certain number of lily bulbs along a pathway. Then, Borya came and planted a new bulb between each pair of adjacent bulbs planted by Аня. After that, Vika came and planted a new bulb between each pair of adjacent bulbs planted before her. Finally, Gosh came and did the same. In the end, 129 lilies bloomed. We need to determine how many bulbs Аня initially planted.

Solution

Let's assume that Аня initially planted x bulbs.

After Borya planted a new bulb between each pair of adjacent bulbs planted by Аня, the total number of bulbs became 2x+1.

After Vika planted a new bulb between each pair of adjacent bulbs planted before her, the total number of bulbs became 4x+3.

After Gosh planted a new bulb between each pair of adjacent bulbs planted before him, the total number of bulbs became 8x+7.

Since 129 lilies bloomed in the end, we can set up the equation:

8x + 7 = 129

Now, let's solve the equation to find the value of x.

8x = 129 - 7

8x = 122

x = 122 / 8

x = 15.25

Since the number of bulbs cannot be a fraction, we can conclude that Аня initially planted 15 bulbs.

Answer

Аня initially planted 15 lily bulbs.

Explanation

Аня initially planted x bulbs. Borya planted a new bulb between each pair of adjacent bulbs planted by Аня, Vika did the same, and Gosh also did the same. In the end, 129 lilies bloomed. By setting up the equation 8x + 7 = 129 and solving for x, we find that Аня initially planted 15 lily bulbs.