Question

Ваня решил подарить Маше на день рождения букет из нечетного числа цветов, состоящего из желтых и красных тюльпанов, так чтобы количество цветов одного цвета отличалось от количества цветов другого ровно на один. Желтые тюльпаны стоят 50 рублей за штуку, а красные ‑ 31 рубль. Из какого наибольшего числа тюльпанов он может купить букет Маше на день рождения, потратив не более 600 рублей?

Answer 1

8 красных 
7 желтых 
Если проверить то остается 3 рубля еще 

Answer 2

Answer in detail. Vanya decided to give Masha a bouquet of an odd number of flowers for her birthday, consisting of yellow and red tulips, so that the number of flowers of one color differed from the number of flowers of another by exactly one. Yellow tulips cost 50 rubles apiece, and red ones cost 31 rubles. How many tulips can he buy for Masha's birthday bouquet, spending no more than 600 rubles?

To answer this question, we need to find the maximum odd number of tulips that Vanya can buy with 600 rubles, such that the difference between the number of yellow and red tulips is one. Let x be the number of yellow tulips and y be the number of red tulips. Then we have the following equations:

x + y = n (where n is an odd number) x - y = 1 50x + 31y = 600

We can solve this system of equations by substitution or elimination. For example, by substituting x = y + 1 into the third equation, we get:

50(y + 1) + 31y = 600 81y + 50 = 600 81y = 550 y = 6.79

Since y must be an integer, we round it down to 6. Then x = y + 1 = 7. Therefore, Vanya can buy 7 yellow tulips and 6 red tulips for Masha's birthday bouquet, spending 50 * 7 + 31 * 6 = 581 rubles. The number of tulips is 7 + 6 = 13, which is the maximum odd number that satisfies the conditions.