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We are given two investment ratios:

1. The ratio of Amara's investment to Bina's is \( 1:3 \).
2. The ratio of Bina's investment to Collette's is \( 4:5 \).

To find the overall ratio of Amara : Bina : Collette, we need to combine these two ratios. Let's proceed step by step:

- From the first ratio, we know \( A : B = 1:3 \).
- From the second ratio, we know \( B : C = 4:5 \).

To combine these ratios, the values for \( B \) (Bina) must be the same in both ratios. In the first ratio \( A : B = 1:3 \), \( B \) is 3. In the second ratio \( B : C = 4:5 \), \( B \) is 4.

The least common multiple (LCM) of 3 and 4 is 12. So, we need to adjust both ratios such that \( B = 12 \).

- Multiply the first ratio \( A : B = 1:3 \) by 4 to get \( A : B = 4:12 \).
- Multiply the second ratio \( B : C = 4:5 \) by 3 to get \( B : C = 12:15 \).

Now, we can combine these ratios:

- Amara : Bina : Collette \( = 4 : 12 : 15 \).

Thus, the correct investment ratio is **4:12:15**, which corresponds to option **d**.

Would you like more details or have any other questions?

Here are 5 related questions to explore:
1. How do you find the least common multiple (LCM) of two numbers?
2. What is the method for combining multiple ratios into one?
3. How would you solve the problem if the second ratio had been different, e.g., \( B : C = 5:6 \)?
4. Can ratios be simplified similarly to fractions, and how?
5. How can this method be applied to other real-life scenarios, such as recipe adjustments?

**Tip**: When combining ratios, always ensure that the shared term is the same across both ratios before merging.

Amara, Bina, and Collette invested their savings in a bank. The ratio of the investment of Amara's to Bina's is 1:3 and that of Bina's to Collette's is 4:5. What is the investment ratio of Amara: Bina: Collette?

This problem explains how to combine two investment ratios (1:3 and 4:5) using the least common multiple (LCM) to find the final investment ratio of Amara, Bina, and Collette. Suitable for students in Grades 6-8.

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