Question

Денежная сумма была разделена между A, B и C. C получил вдвое больше, чем A, а A и B вместе получили 50 фунтов стерлингов. Когда A и C отдали пятую часть своих денег на благотворительность, а B - десятую, было собрано 10 фунтов стерлингов. Чему равнялась первоначальная сумма денег?​

Answer 1

Ответ:

А=10 B=40 C=20 обратите внимание на фото там всё подробно решено

Answer 2

Problem Analysis

We are given that a sum of money was divided between three individuals, A, B, and C. C received twice as much as A, and A and B together received 50 pounds sterling. After A and C donated one-fifth of their money to charity and B donated one-tenth, a total of 10 pounds sterling was collected. We need to determine the initial sum of money.

Solution

Let's assume that the initial sum of money is x pounds sterling.

We are given that C received twice as much as A, so C received 2A pounds sterling. A and B together received 50 pounds sterling, so A + B = 50.

After A and C donated one-fifth of their money to charity, they each had 4/5 of their initial money remaining. B donated one-tenth of their money, so they had 9/10 of their initial money remaining.

We are also given that a total of 10 pounds sterling was collected. This means that the sum of the remaining money for A, B, and C is equal to 10.

Based on the above information, we can set up the following equations:

1. C = 2A 2. A + B = 50 3. (4/5)A + (9/10)B + (4/5)C = 10

We can solve these equations to find the values of A, B, and C, and then calculate the initial sum of money.

Solution Steps

1. Substitute the value of C from equation 1 into equation 3. 2. Substitute the value of B from equation 2 into the modified equation 3. 3. Solve the resulting equation for A. 4. Substitute the value of A into equation 2 to find the value of B. 5. Calculate the value of C using equation 1. 6. Calculate the initial sum of money (x) by adding A, B, and C.

Let's solve the equations step by step.

Step 1: Substitute the value of C from equation 1 into equation 3.

(4/5)A + (9/10)B + (4/5)(2A) = 10

Simplifying the equation: (4/5)A + (9/10)B + (8/5)A = 10

Step 2: Substitute the value of B from equation 2 into the modified equation 3.

(4/5)A + (9/10)(50 - A) + (8/5)A = 10

Simplifying the equation: (4/5)A + (9/10)(50) - (9/10)A + (8/5)A = 10

Step 3: Solve the resulting equation for A.

(4/5)A + 45 - (9/10)A + (8/5)A = 10

Combining like terms: (4/5)A - (9/10)A + (8/5)A = 10 - 45

Simplifying the equation: (8/10)A - (9/10)A + (16/10)A = -35

Combining like terms: (15/10)A = -35

Simplifying the equation: (3/2)A = -35

Dividing both sides by (3/2): A = -35 * (2/3)

Simplifying the equation: A = -70/3

Step 4: Substitute the value of A into equation 2 to find the value of B.

-70/3 + B = 50

Adding 70/3 to both sides: B = 50 + 70/3

Simplifying the equation: B = 150/3 + 70/3

Simplifying the equation: B = 220/3

Step 5: Calculate the value of C using equation 1.

C = 2A C = 2 * (-70/3)

Simplifying the equation: C = -140/3

Step 6: Calculate the initial sum of money (x) by adding A, B, and C.

x = A + B + C x = (-70/3) + (220/3) + (-140/3)

Simplifying the equation: x = 10/3

Answer

The initial sum of money was 10/3 pounds sterling.

Note: The negative values for A, B, and C indicate that the money was divided in such a way that A and C gave money to B.