Question

На новогодний праздник в школу завезли три вида мороженого: шоколадное, клубничное и ванильное. Шоколадное составляло 52% массы всего мороженого, клубничное - 25% массы шоколадного, а ванильное - остальные 140 кг. Сколько килограммов мороженого завезли в школу? Даю 25 баллов.

Answer 1

Calculation of the Total Weight of Ice Cream

To calculate the total weight of ice cream brought to the school, we need to determine the weight of each flavor and then add them together.

Let's denote the weight of chocolate ice cream as C, the weight of strawberry ice cream as S, and the weight of vanilla ice cream as V.

According to the information given, the weight of chocolate ice cream is 52% of the total weight of all ice cream. This can be expressed as:

C = 0.52 × (C + S + V)

The weight of strawberry ice cream is 25% of the weight of chocolate ice cream. This can be expressed as:

S = 0.25 × C

Finally, the weight of vanilla ice cream is the remaining 140 kg, which means:

V = 140 kg

To find the total weight of ice cream, we can substitute the values of C, S, and V into the equation:

Total weight = C + S + V

Let's solve these equations to find the weight of ice cream brought to the school.

Solution:

1. From the given information, we know that the weight of vanilla ice cream is 140 kg. 2. We can calculate the weight of strawberry ice cream using the equation S = 0.25 × C. 3. We can calculate the weight of chocolate ice cream using the equation C = 0.52 × (C + S + V).

Let's solve these equations step by step:

1. Substitute the value of V into the equation C = 0.52 × (C + S + V): C = 0.52 × (C + S + 140)

2. Substitute the value of S from the equation S = 0.25 × C into the above equation: C = 0.52 × (C + 0.25 × C + 140)

3. Simplify the equation: C = 0.52 × (1.25 × C + 140)

4. Distribute the multiplication: C = 0.65 × C + 72.8

5. Subtract 0.65 × C from both sides of the equation: C - 0.65 × C = 72.8

6. Simplify the equation: 0.35 × C = 72.8

7. Divide both sides of the equation by 0.35 to solve for C: C = 72.8 / 0.35

Using a calculator, we find that C ≈ 208 kg.

Now that we know the weight of chocolate ice cream, we can calculate the weight of strawberry ice cream:

S = 0.25 × C ≈ 0.25 × 208 kg ≈ 52 kg

Finally, we can calculate the total weight of ice cream:

Total weight = C + S + V ≈ 208 kg + 52 kg + 140 kg ≈ 400 kg

Therefore, approximately 400 kilograms of ice cream were brought to the school for the New Year holiday.

I hope this helps! Let me know if you have any further questions.