25 2025 Assessment of Grade 5 Mathematics (Marks: 100) At the end of this specific assignment, students should be able to: - Calculate the answers to Grade 5 Patterns, Functions, and Algebra problems. - Describe how the answer was obtained in selected cases - Critically examine the conceptual development of patterns, functions, and algebra from Grades 4 to 6. - Demonstrate the progression of conceptual complexity by designing a series of activities on the same topic. - Determine the value of different functions using the relevant calculations and manipulations. - Explain the different terminology involved with expressions and solving equations - Solve a number of equations. Question 1 (Marks: 30) Multiple Choice Read the question below and choose the correct answer for each question. You can only choose one letter for each question. Example: Q.1.1. A - You may use a calculator. - All calculations or reasonings for your answer must be included. Q.1.1 In a string of beads, there are two red beads for every five green beads and three (3) purple beads for every 10 green beads. How many purple beads are there in a string with 12 red beads? A. 50 B. 10 C. 9 D. 15 E. 18 © The Independent Institute of Education (Pty) Ltd 2025 Page 3 of 12

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UpStudy AI · Accepted Answer

To solve the problem, we need to analyze the relationships between the different colored beads based on the information provided.

### Known Conditions:
1. There are 2 red beads for every 5 green beads.
2. There are 3 purple beads for every 10 green beads.
3. We have 12 red beads in total.

### Step-by-Step Solution:

1. **Determine the number of green beads based on red beads:**
   - The ratio of red beads to green beads is $$ \frac{2}{5} $$.
   - Let $$ r $$ be the number of red beads and $$ g $$ be the number of green beads.
   - From the ratio, we can set up the equation:
     $$
     \frac{r}{g} = \frac{2}{5}
     $$
   - Substituting $$ r = 12 $$:
     $$
     \frac{12}{g} = \frac{2}{5}
     $$
   - Cross-multiplying gives:
     $$
     2g = 12 \times 5
     $$
     $$
     2g = 60
     $$
     $$
     g = \frac{60}{2} = 30
     $$
   - Therefore, there are 30 green beads.

2. **Determine the number of purple beads based on green beads:**
   - The ratio of purple beads to green beads is $$ \frac{3}{10} $$.
   - Let $$ p $$ be the number of purple beads.
   - From the ratio, we can set up the equation:
     $$
     \frac{p}{g} = \frac{3}{10}
     $$
   - Substituting $$ g = 30 $$:
     $$
     \frac{p}{30} = \frac{3}{10}
     $$
   - Cross-multiplying gives:
     $$
     10p = 3 \times 30
     $$
     $$
     10p = 90
     $$
     $$
     p = \frac{90}{10} = 9
     $$
   - Therefore, there are 9 purple beads.

### Conclusion:
The number of purple beads in a string with 12 red beads is **9**.

### Final Answer:
Q.1.1. C
There are 9 purple beads in the string. **Answer:** C

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