Amanda, Brandon and Charlene shared the cost for a present. Amandas share of the cost to Brandons share of the cost was 4 : 5. Brandons share of the cost to Charlenes 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? calulate this in a simple short way  

Let Amanda's share, Brandon's share, and Charlene's share of the cost be denoted as \( A \), \( B \), and \( C \), respectively.

We are given:
1. The ratio of Amanda's share to Brandon's share: \( A : B = 4 : 5 \), which means \( A = \frac{4}{5}B \).
2. The ratio of Brandon's share to Charlene's share: \( B : C = 2 : 3 \), which means \( C = \frac{3}{2}B \).
3. Amanda and Charlene together gave \( R46 \), so \( A + C = 46 \).

### Step-by-step solution:
Substitute the expressions for \( A \) and \( C \) in terms of \( B \) into the equation \( A + C = 46 \):
\[
\frac{4}{5}B + \frac{3}{2}B = 46.
\]
Now, solve this equation for \( B \).

1. Find a common denominator for the fractions \( \frac{4}{5} \) and \( \frac{3}{2} \). The least common denominator is 10, so rewrite the equation:
\[
\frac{8}{10}B + \frac{15}{10}B = 46.
\]
2. Combine the fractions:
\[
\frac{23}{10}B = 46.
\]
3. Solve for \( B \):
\[
B = 46 \times \frac{10}{23} = 20.
\]

Now that we have \( B = 20 \), we can find \( A \) and \( C \):
- \( A = \frac{4}{5} \times 20 = 16 \),
- \( C = \frac{3}{2} \times 20 = 30 \).

### Total cost of the present:
The total cost is \( A + B + C = 16 + 20 + 30 = 66 \).

So, the cost of the present is **R66**.

Would you like further details or clarification on any step?

Here are 5 related questions for further exploration:
1. What if Amanda and Brandon's share ratio changed to 3:5?
2. How would the total cost change if Charlene's contribution was reduced by 10%?
3. Can we solve this problem using a different approach, like assuming variables for each share from the start?
4. How does this problem relate to the concept of proportion in mathematics?
5. What happens if Amanda and Charlene together contributed R50 instead?

**Tip:** When working with ratios, always ensure to express each term in terms of the same variable before solving.

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 problem involving the ratio of cost-sharing between Amanda, Brandon, and Charlene. This detailed solution explains how to use ratios and algebra to find the total cost of the present. Suitable for students in Grades 8-10.

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