Question

Сумма трёх чисел 480. первое число составляет 32 °/• суммы. а второе 41°/• найдите третье число 2)товар подорожал на22 °/• и его цена составляет теперь 488 руб. какой была цена изначально

Answer 1

32%=0,32
480:0,32=1500
41%=0,41
480:0,41

Answer 2

1+2+3=480
1=x , 2=y , 3=z
x=480*0.32---->x=153.6
y=480*0.41---->y=196.8
z=129.6

Answer 3

Problem 1: Finding the Third Number

To find the third number, we need to solve the equation where the sum of three numbers is 480, and the first number is 32% of the sum, and the second number is 41% of the sum.

Let's denote the first number as x, the second number as y, and the third number as z.

According to the given information, we have the following equations:

1. x + y + z = 480 (equation 1) 2. x = 0.32 * (x + y + z) (equation 2) 3. y = 0.41 * (x + y + z) (equation 3)

We can solve this system of equations to find the values of x, y, and z.

Solution to Problem 1:

Let's solve the system of equations using substitution.

From equation 2, we have x = 0.32 * (x + y + z). Expanding the equation, we get: x = 0.32x + 0.32y + 0.32z

Rearranging the terms, we get: 0.68x = 0.32y + 0.32z (equation 4)

Similarly, from equation 3, we have y = 0.41 * (x + y + z). Expanding the equation, we get: y = 0.41x + 0.41y + 0.41z

Rearranging the terms, we get: 0.59y = 0.41x + 0.41z (equation 5)

Now, let's substitute equations 4 and 5 into equation 1 to eliminate x and y.

Substituting equation 4 into equation 1, we get: 0.68x + y + z = 480

Substituting equation 5 into equation 1, we get: x + 0.59y + z = 480

Combining the two equations, we get: 0.68x + y + z = x + 0.59y + z

Simplifying the equation, we get: 0.68x - x = 0.59y - y

0.32x = 0.41y

Dividing both sides by 0.32, we get: x = (0.41/0.32)y

x = 1.28125y (equation 6)

Now, let's substitute equation 6 into equation 4 to find the relationship between x and z.

Substituting equation 6 into equation 4, we get: 0.68(1.28125y) = 0.32y + 0.32z

Simplifying the equation, we get: 0.87125y = 0.32y + 0.32z

Subtracting 0.32y from both sides, we get: 0.55125y = 0.32z

Dividing both sides by 0.32, we get: z = (0.55125/0.32)y

z = 1.72265625y (equation 7)

Now, let's substitute equations 6 and 7 into equation 1 to find the value of y.

Substituting equations 6 and 7 into equation 1, we get: 1.28125y + y + 1.72265625y = 480

Combining like terms, we get: 4.00490625y = 480

Dividing both sides by 4.00490625, we get: y = 120

Now, let's substitute the value of y into equations 6 and 7 to find the values of x and z.

Substituting y = 120 into equation 6, we get: x = 1.28125 * 120 x = 153.75

Substituting y = 120 into equation 7, we get: z = 1.72265625 * 120 z = 207.1875

Therefore, the first number is 153.75, the second number is 120, and the third number is 207.1875.

Answer to Problem 1:

The first number is 153.75, the second number is 120, and the third number is 207.1875.

Problem 2: Finding the Original Price

To find the original price of the item, we need to calculate the price before the 22% increase.

Let's denote the original price as x.

According to the given information, the price after the 22% increase is 488 rubles.

We can use the formula for calculating the original price after a percentage increase:

Original Price = Price After Increase / (1 + Percentage Increase)

Let's substitute the given values into the formula and solve for the original price.

Solution to Problem 2:

Using the formula for calculating the original price after a percentage increase, we have:

Original Price = 488 / (1 + 0.22)

Calculating the expression, we get:

Original Price = 488 / 1.22 Original Price ≈ 400

Therefore, the original price of the item was approximately 400 rubles.

Answer to Problem 2:

The original price of the item was approximately 400 rubles.