https://file.aiquickdraw.com/mathbot/file/1726410055855zsphehli.jpg

Let's work through the problem step by step.

### Given Data:
- The density of apple juice is \( 1.04 \, \text{g/cm}^3 \).
- The density of fruit syrup is \( 1.6 \, \text{g/cm}^3 \).
- The density of sparkling water is \( 0.99 \, \text{g/cm}^3 \).

- Volume of apple juice: \( 35 \, \text{cm}^3 \)
- Volume of fruit syrup: \( 25 \, \text{cm}^3 \)
- Volume of sparkling water: \( 270 \, \text{cm}^3 \)

Total volume of the mixture: \( 330 \, \text{cm}^3 \)

### Step 1: Calculate the mass of each component
1. **Mass of apple juice**:
   \[
   \text{Mass of apple juice} = \text{Density} \times \text{Volume} = 1.04 \times 35 = 36.4 \, \text{g}
   \]

2. **Mass of fruit syrup**:
   \[
   \text{Mass of fruit syrup} = \text{Density} \times \text{Volume} = 1.6 \times 25 = 40 \, \text{g}
   \]

3. **Mass of sparkling water**:
   \[
   \text{Mass of sparkling water} = \text{Density} \times \text{Volume} = 0.99 \times 270 = 267.3 \, \text{g}
   \]

### Step 2: Calculate the total mass of the drink
\[
\text{Total mass} = 36.4 + 40 + 267.3 = 343.7 \, \text{g}
\]

### Step 3: Calculate the density of the drink
The density of the drink is given by:
\[
\text{Density of the drink} = \frac{\text{Total mass}}{\text{Total volume}} = \frac{343.7}{330} \approx 1.041 \, \text{g/cm}^3
\]

So, the density of the drink is **1.041 g/cm³**, correct to three decimal places.

Would you like further details or have any questions?

### Relative questions:
1. How does the density of a mixture relate to the individual densities of its components?
2. Why is it important to know the density of a drink in real-world scenarios?
3. What would happen to the density if we increased the amount of fruit syrup?
4. Can the density of a mixture ever be lower than the lowest density component?
5. How would you calculate the mass if the density and volume are given but in different units?

### Tip:
Always ensure the units are consistent (such as g/cm³) when calculating densities or any related quantities!

The density of apple juice is 1.04 grams per cm³. The density of fruit syrup is 1.6 grams per cm³. The density of sparkling water is 0.99 grams per cm³. 35 cm³ of apple juice are mixed with 25 cm³ of fruit syrup and 270 cm³ of sparkling water to make a drink with a volume of 330 cm³. Work out the density of the drink. Give your answer correct to 3 decimal places.

Learn how to calculate the density of a drink mixture containing apple juice, fruit syrup, and sparkling water. This problem includes calculations of mass and volume to determine the density of the drink to three decimal places. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation