Question

В букете 19 красных желтых и белых гладиолусов . Красных гладиолусов в 3 раза больше чем белых а желтых больше , чем белых, но меньше, чем красных . сколько желтых гладиолусов в букете? Сравните кол- во красных , желтых , и белых гладиолусов . Результат сравнения запишите в виде двойного неравенства

Answer 1

Обозначим число белых гладиолусов за Х, тогда красных, раз их в три раза больше будет 3Х, значит, желтых, то что осталось, т.е. (19-Х-3Х)=(19-4Х).
Запишем результат сравнения в виде двойного неравенства: X<(19-4X)<3X. (Из условия)
Рассмотрим неравенства.
1. Х<(19-4Х); ⇒(4Х+Х)<19; 5Х<19; Х<19/5;  Х<3ц4/5 (1)
2. (19-4Х)<3X; ⇒19<(3Х+4Х); 19<7X ⇒ X>19/7; X>2ц4/7 (2)
Запишем, исходя из (1) и (2) двойное неравенство: 3ц4/5>X>2ц4/7. Т.к. количество гладиолусов каждого цвета - это целое число (про сломанные в условии не было сказано!), то ясно,что только число Х=3 может соответствовать   количеству белых гладиолусов. Тогда число красных: 3Х=3·3=9 (гладиолусов), а желтых: (19-3-9)=7(гладиолусов)
Ответ: 3 белых гладиолуса, 9 красных, 7 желтых.Сравнение: 3<7<9.

Answer 2

Problem Analysis

We are given a bouquet of gladiolus flowers consisting of 19 flowers in total. The bouquet contains red, yellow, and white gladiolus flowers. The number of red flowers is three times the number of white flowers, and the number of yellow flowers is more than the number of white flowers but less than the number of red flowers. We need to determine the number of yellow gladiolus flowers in the bouquet and compare the quantities of red, yellow, and white flowers using a double inequality.

Solution

Let's assume the number of white gladiolus flowers in the bouquet is x.

According to the given information: - The number of red gladiolus flowers is three times the number of white flowers, so the number of red flowers is 3x. - The number of yellow gladiolus flowers is more than the number of white flowers but less than the number of red flowers. Therefore, the number of yellow flowers is between x and 3x.

To find the number of yellow gladiolus flowers, we need to solve the inequality x < yellow flowers < 3x.

Calculation

Let's solve the inequality to find the range of possible values for the number of yellow gladiolus flowers:

x < yellow flowers < 3x

Since the number of flowers in the bouquet is 19, we can write the equation:

x + yellow flowers + 3x = 19

Simplifying the equation:

4x + yellow flowers = 19

Now, we can substitute the possible values for x and calculate the range of possible values for the number of yellow gladiolus flowers.

Let's consider a few possible values for x:

1. If x = 1, then 4(1) + yellow flowers = 19. Solving this equation, we find that yellow flowers = 15. 2. If x = 2, then 4(2) + yellow flowers = 19. Solving this equation, we find that yellow flowers = 11. 3. If x = 3, then 4(3) + yellow flowers = 19. Solving this equation, we find that yellow flowers = 7.

Therefore, the number of yellow gladiolus flowers in the bouquet can be either 15, 11, or 7.

Comparison of Quantities

To compare the quantities of red, yellow, and white gladiolus flowers, we can use the following double inequality:

white flowers < yellow flowers < red flowers

Substituting the values we found earlier:

x < 15, 11, 7 < 3x

Since we don't have a specific value for x, we can't determine the exact quantities of white, yellow, and red flowers. However, we know that the number of yellow flowers is between 7 and 15, and the number of red flowers is three times the number of white flowers.

Conclusion

In conclusion, the number of yellow gladiolus flowers in the bouquet can be either 15, 11, or 7. The exact quantities of white, yellow, and red flowers cannot be determined without knowing the specific value of x. However, we know that the number of yellow flowers is between 7 and 15, and the number of red flowers is three times the number of white flowers.