Let's break down the problem step by step.

Step 1: Express the ratios as fractions

• Amanda's share to Brandon's share is given as $\frac{4}{5}$.
• Brandon's share to Charlene's share is given as $\frac{2}{3}$.

Step 2: Determine the relationships between their shares

Let's assign variables to their shares:

• Let Amanda's share be $A$.
• Let Brandon's share be $B$.
• Let Charlene's share be $C$.

From the first ratio: $\frac{A}{B} = \frac{4}{5}$ This implies: $A = \frac{4}{5}B \quad \text{(Equation 1)}$

From the second ratio: $\frac{B}{C} = \frac{2}{3}$ This implies: $B = \frac{2}{3}C \quad \text{(Equation 2)}$

Step 3: Substitute the value of $B$ from Equation 2 into Equation 1

Substitute $B = \frac{2}{3}C$ into $A = \frac{4}{5}B$: $A = \frac{4}{5} \times \frac{2}{3}C = \frac{8}{15}C$

So, Amanda's share $A$ is $\frac{8}{15}C$.

Step 4: Use the total amount Amanda and Charlene contributed

We are told that Amanda and Charlene together contributed R46: $A + C = 46$

Substituting $A = \frac{8}{15}C$ into this equation: $\frac{8}{15}C + C = 46$

Step 5: Solve for $C$

To combine the terms, express $C$ as $\frac{15}{15}C$: $\frac{8}{15}C + \frac{15}{15}C = 46$ $\frac{23}{15}C = 46$

Now, multiply both sides by $\frac{15}{23}$ to solve for $C$: $C = 46 \times \frac{15}{23} = 30$

Step 6: Find the total cost of the present

Now that we know Charlene's share $C = 30$, we can find the shares of Amanda and Brandon:

• Amanda's share $A = \frac{8}{15} \times 30 = 16$.
• Brandon's share $B = \frac{2}{3} \times 30 = 20$.

Finally, the total cost of the present is: $A + B + C = 16 + 20 + 30 = 66$

Conclusion

The total cost of the present was R66.

Would you like further details, or do you have any questions?

---

Related Questions:

1. If the total amount Amanda and Brandon contributed together was given, how would you calculate Charlene's share?
2. What if the ratio between Amanda and Charlene was different? How would that affect the total cost?
3. How can you verify the correctness of these ratios in real-life scenarios?
4. How would the total cost change if Amanda's contribution was increased by a fixed amount?
5. What if only the ratio of Amanda's share to the total cost was given? How would you solve for the other shares?

Tip: Always cross-check the ratios given in problems like these to ensure you set up the correct relationships before solving.