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.