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Let's break down the problem to find the correct investment ratio for Amara, Bina, and Collette:

We are given two ratios:
1. The ratio of Amara's investment to Bina's is \( 1:3 \), so we can write this as:
   \[
   A : B = 1 : 3
   \]
2. The ratio of Bina's investment to Collette's is \( 4:5 \), which can be written as:
   \[
   B : C = 4 : 5
   \]

### To combine these ratios:

- From the first ratio \( A : B = 1 : 3 \), we can express Bina's investment \( B \) as \( 3 \times A \) (i.e., \( B = 3A \)).
- From the second ratio \( B : C = 4 : 5 \), we know \( B = 4k \) and \( C = 5k \).

To make the ratios compatible, we need to align the value of \( B \) in both expressions. From the first expression, \( B = 3A \), and from the second expression, \( B = 4k \).

Thus, set \( 3A = 4k \), giving us:
\[
A = \frac{4k}{3}
\]

Now substitute this into \( B = 4k \) and \( C = 5k \):

- \( A = \frac{4k}{3} \)
- \( B = 4k \)
- \( C = 5k \)

To get rid of the fraction, multiply all three terms by 3:
\[
A : B : C = \left(\frac{4k}{3} \times 3\right) : (4k \times 3) : (5k \times 3)
\]
This simplifies to:
\[
A : B : C = 4 : 12 : 15
\]

Thus, the investment ratio of Amara, Bina, and Collette is \( \boxed{4 : 12 : 15} \), which corresponds to option **d**.

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Do you need further details on this? Here are five related questions you can explore:

1. How do you simplify ratios involving fractions?
2. What are the methods to solve problems with multiple ratios?
3. How can ratios help in solving real-world investment problems?
4. What is the importance of finding a common factor in combining ratios?
5. How can proportions be used to scale investments fairly?

**Tip**: Always find a common term when combining two ratios, to align the variables efficiently.

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?

Solve the investment ratio problem where Amara, Bina, and Collette invested their savings with given ratios. This problem involves the use of ratios and proportions to find the correct investment ratio of 4:12:15, suitable for students in Grades 6-8.

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