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?

Let the cost shares of Amanda, Brandon, and Charlene be represented by \( A \), \( B \), and \( C \) respectively.

From the problem, we have the following information:
- Amanda's share to Brandon's share is \( 4:5 \), which gives the equation:
  \[
  \frac{A}{B} = \frac{4}{5}, \quad \text{or equivalently} \quad A = \frac{4}{5}B.
  \]
- Brandon's share to Charlene's share is \( 2:3 \), which gives the equation:
  \[
  \frac{B}{C} = \frac{2}{3}, \quad \text{or equivalently} \quad B = \frac{2}{3}C.
  \]
- Amanda and Charlene together gave R46, which gives the equation:
  \[
  A + C = 46.
  \]

### Step 1: Express everything in terms of \( C \)
From \( B = \frac{2}{3}C \), we can substitute this into the equation \( A = \frac{4}{5}B \):
\[
A = \frac{4}{5} \times \frac{2}{3}C = \frac{8}{15}C.
\]
Now substitute this into the equation \( A + C = 46 \):
\[
\frac{8}{15}C + C = 46.
\]

### Step 2: Solve for \( C \)
Combine the terms on the left-hand side:
\[
\frac{8}{15}C + \frac{15}{15}C = 46,
\]
\[
\frac{23}{15}C = 46.
\]
Multiply both sides by 15 to eliminate the fraction:
\[
23C = 46 \times 15,
\]
\[
23C = 690.
\]
Now divide both sides by 23:
\[
C = \frac{690}{23} = 30.
\]

### Step 3: Calculate \( B \) and \( A \)
- \( B = \frac{2}{3}C = \frac{2}{3} \times 30 = 20 \).
- \( A = \frac{8}{15}C = \frac{8}{15} \times 30 = 16 \).

### Step 4: Find the total cost of the present
The total cost of the present is \( A + B + C \):
\[
A + B + C = 16 + 20 + 30 = 66.
\]

Thus, the total cost of the present is **R66**.

Would you like a breakdown of any step or further details?

Here are 5 related questions:
1. What if Amanda’s share was in the ratio 3:5 instead of 4:5?
2. How would the solution change if Amanda and Charlene gave R50 instead of R46?
3. How can you generalize the solution for different ratios between Brandon and Charlene?
4. What is the share distribution if the total cost was R80 instead of R66?
5. What would happen if all three shared equally instead of using the given ratios?

**Tip:** When working with ratios, converting them to algebraic expressions helps in forming equations and solving them systematically.

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?

Solve the problem where Amanda, Brandon, and Charlene share the cost of a present using ratios. Learn how to set up and solve equations involving ratios to find the total cost. This problem is suitable for students in Grades 8-10 and covers key algebraic concepts, including solving linear equations.

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