Question

В гирлянде были синие, желтые и красные шары. 3/4 всех шаров в гирлянде без 9 шаров были синими. 1/2 оставшихся шаров и 3 шара были желтыми, а остальные 5 шаров были красными. сколько шаров в гирлянде? сколько синих шаров в гирлянде?

Answer 1

В гирлянде были синие, желтые и красные шары. 3/4 всех шаров в гирлянде без 9 шаров были синими. 1/2 оставшихся шаров и 3 шара были желтыми, а остальные 5 шаров были красными. сколько шаров в гирлянде? сколько синих шаров в гирлянде?

Решение

примем

х1 - количество синих шаров в гирлянде, шт

х2 - количество желтых шаров в гирлянде, шт

х3 - количество красных шаров в гирлянде, шт

х - общее количество шаров в гирлянде, шт

тогда

х1=х*3/4-9

х2=(х-(х*3/4-9))*1/2+3

х3=5

х=х1+х2+х3

х*3/4-9+(х-(х*3/4-9))*1/2+3+5=х

х*3/4-9+х*1/2-(х*3/4)*1/2+9*1/2+3+5=х

х-х*3/4-х*1/2+(х*3/4)*1/2 =-9+9*1/2+8

х*1/4-х*1/2+х*3/8 =3,5

(2*х-4*х+3*х)/8=3,5

х=3,5*8

х=28 шт - всего шаров в гирлянде

х1=28*3/4-9 = 12 шт - синих шаров в гирлянде

Проверим

х2=(28-12)*1/2+3=11шт - желтых шаров в гирлянде

28-12-11=5 шт - остальных красных шаров

5=5 -решение истино

Ответ:

28 шт - всего шаров в гирлянде

12 шт - синих шаров в гирлянде

 

 

 

 

Answer 2

Problem Analysis

We are given a garland with blue, yellow, and red balls. We know that 3/4 of all the balls in the garland, excluding 9 balls, are blue. Additionally, 1/2 of the remaining balls, plus 3 balls, are yellow, and the remaining 5 balls are red. We need to determine the total number of balls in the garland and the number of blue balls.

Solution

Let's assume the total number of balls in the garland is x.

From the given information, we can form the following equations:

1. 3/4 of all the balls in the garland, excluding 9 balls, are blue: - (3/4)(x - 9) = blue balls

2. 1/2 of the remaining balls, plus 3 balls, are yellow: - (1/2)(x - 9 - blue balls) + 3 = yellow balls

3. The remaining 5 balls are red: - red balls = 5

To solve this system of equations, we can substitute equation 1 into equation 2 and equation 2 into equation 3.

Substituting equation 1 into equation 2: - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = yellow balls

Substituting equation 2 into equation 3: - red balls = 5

Now, we can solve for the number of blue balls and the total number of balls in the garland.

Calculation

Let's solve the equations step by step:

1. Substituting equation 1 into equation 2: - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = yellow balls - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x - 9)) + 3 = (1/2)(x - 9 - (3/4)(x - 9)) + 3 - (1/2)(x - 9 - (3/4)(x