Amanda, Brandon and Charlene shared the cost for a present. Amanda`s share of the cost to Brandon`s share of the cost was 4 : 5. Brandon`s share of the cost to Charlene`s share of the cost was 2 : 3. Amanda and Charlene gave a total of R46 for the present. What was the cost of the present?

We are given that Amanda, Brandon, and Charlene shared the cost for a present. Here’s a breakdown of the given information:

1. **Amanda's share to Brandon's share** is \(4:5\).
2. **Brandon's share to Charlene's share** is \(2:3\).
3. Amanda and Charlene together contributed \(R46\).

To solve this, we need to find the total cost of the present.

### Step 1: Express Amanda, Brandon, and Charlene’s shares in terms of a common variable
- Let Amanda's share be \(4x\), and Brandon's share be \(5x\) based on the ratio \(4:5\).
- Now, we need to link Brandon's share to Charlene's share using the ratio \(2:3\). Since Brandon's share is \(5x\), and the ratio of Brandon to Charlene is \(2:3\), Charlene's share can be written as:
\[
\frac{B}{C} = \frac{2}{3} \Rightarrow C = \frac{3}{2}B = \frac{3}{2}(5x) = \frac{15x}{2}
\]

Thus, the shares are:
- Amanda's share = \(4x\)
- Brandon's share = \(5x\)
- Charlene's share = \(\frac{15x}{2}\)

### Step 2: Use the information about Amanda and Charlene’s total contribution
We are told that Amanda and Charlene together contributed \(R46\). Therefore, their combined share is:
\[
4x + \frac{15x}{2} = 46
\]
To simplify this equation, multiply through by 2 to eliminate the fraction:
\[
2(4x) + 15x = 92
\]
\[
8x + 15x = 92
\]
\[
23x = 92
\]
\[
x = 4
\]

### Step 3: Find the total cost of the present
Now that we know \(x = 4\), we can calculate each person’s share:
- Amanda’s share = \(4x = 4(4) = R16\)
- Brandon’s share = \(5x = 5(4) = R20\)
- Charlene’s share = \(\frac{15x}{2} = \frac{15(4)}{2} = R30\)

Thus, the total cost of the present is:
\[
16 + 20 + 30 = R66
\]

### Conclusion:
The total cost of the present was **R66**.

Would you like further details or explanations on any part? Here are 5 related questions:

1. How can we confirm that the ratios were applied correctly?
2. What if the total amount given by Amanda and Charlene were different?
3. Can you express Charlene's share directly in terms of Amanda's share?
4. How would the solution change if Amanda and Brandon's ratio were \(3:5\)?
5. Could you use a different method to approach the problem?

**Tip:** When working with ratios, always check if the variable terms are consistent across different relationships.

Amanda, Brandon, and Charlene shared the cost for a present. Amanda's share of the cost to Brandon's share of the cost was 4:5. Brandon's share of the cost to Charlene's share of the cost was 2:3. Amanda and Charlene gave a total of R46 for the present. What was the cost of the present?

Learn how to solve a ratio problem where Amanda, Brandon, and Charlene share the cost of a present. Amanda's and Charlene's combined contribution is R46, and the total cost of the present is R66. This detailed solution covers ratios, algebraic expressions, and proportional reasoning. Suitable for students in Grades 8-10.

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