Let's solve the problem step by step.

We are given that:

1. Amanda's share to Brandon's share is in the ratio $4:5$, meaning Amanda's share is $4x$ and Brandon's share is $5x$.
2. Brandon's share to Charlene's share is in the ratio $2:3$, meaning Brandon's share is $2y$ and Charlene's share is $3y$.
3. Amanda and Charlene together contributed R46 for the present.

Our goal is to find the total cost of the present.

Step 1: Establish the relationship between shares

From the information, Brandon's share is expressed in two ways:

• From the Amanda-Brandon ratio: $B = 5x$
• From the Brandon-Charlene ratio: $B = 2y$

Equating these two expressions for Brandon's share: $5x = 2y \quad \text{or} \quad y = \frac{5x}{2}$

Step 2: Express Amanda and Charlene's contributions

Amanda's contribution is $A = 4x$, and Charlene's contribution is $C = 3y$.

Substituting $y = \frac{5x}{2}$ into Charlene's contribution: $C = 3\left(\frac{5x}{2}\right) = \frac{15x}{2}$

Step 3: Use the total contribution

Amanda and Charlene together contributed R46, so: $A + C = 46$ Substitute $A = 4x$ and $C = \frac{15x}{2}$: $4x + \frac{15x}{2} = 46$ Multiply through by 2 to eliminate the fraction: $8x + 15x = 92$ $23x = 92$ $x = 4$

Step 4: Calculate each person's contribution

Now that we have $x = 4$, we can find the individual shares:

• Amanda's share: $A = 4x = 4(4) = 16$
• Brandon's share: $B = 5x = 5(4) = 20$
• Charlene's share: $C = \frac{15x}{2} = \frac{15(4)}{2} = 30$

Step 5: Total cost of the present

The total cost is the sum of Amanda, Brandon, and Charlene's contributions: $\text{Total cost} = A + B + C = 16 + 20 + 30 = 66$

So, the total cost of the present is R66.

Do you want more details or have any questions? Here are some related questions for practice:

1. If Amanda contributed R50, what would be the total cost of the present?
2. How would the total cost change if Charlene's contribution doubled?
3. What is the ratio of the total cost to Amanda's contribution?
4. If Brandon only had R18, what would be Amanda and Charlene’s contributions to make up the difference?
5. How much would each person contribute if the total cost was R90 but the ratios stayed the same?

Tip: In problems with ratios, find a common variable to relate the different ratios together before solving.