We are given three people—Amanda, Brandon, and Charlene—sharing the cost of a present. The following ratios are provided:

1. Amanda's share to Brandon's share = 4:5.
2. Brandon's share to Charlene's share = 2:3.
3. Amanda and Charlene together contributed R46.

Let the amounts contributed by Amanda, Brandon, and Charlene be denoted by $A$, $B$, and $C$, respectively.

Step 1: Express the shares in terms of a common variable

From the first ratio, $A : B = 4 : 5$. This means:

$A = \frac{4}{5}B \quad \text{or equivalently} \quad A = \frac{4}{5}B$

From the second ratio, $B : C = 2 : 3$. This means:

$B = \frac{2}{3}C \quad \text{or equivalently} \quad C = \frac{3}{2}B$

Step 2: Set up the equation based on Amanda and Charlene's contribution

We know that Amanda and Charlene together gave R46. So, we have:

$A + C = 46$

Substitute the expressions for $A$ and $C$ in terms of $B$ into this equation:

$\frac{4}{5}B + \frac{3}{2}B = 46$

Step 3: Solve for $B$

To solve this, find a common denominator for the fractions. The least common denominator of 5 and 2 is 10, so rewrite the equation as:

$\frac{8}{10}B + \frac{15}{10}B = 46$

Now combine the terms on the left-hand side:

$\frac{23}{10}B = 46$

Multiply both sides by 10 to eliminate the denominator:

$23B = 460$

Now divide both sides by 23:

$B = 20$

Step 4: Find the total cost of the present

Now that we know Brandon's share $B = 20$, we can find Amanda's and Charlene's contributions:

• Amanda's share: $A = \frac{4}{5} \times 20 = 16$
• Charlene's share: $C = \frac{3}{2} \times 20 = 30$

The total cost of the present is:

$A + B + C = 16 + 20 + 30 = 66$

Thus, the total cost of the present is R66.

Would you like a detailed breakdown of any step or have any other questions?

Here are some related questions for you:

1. How would the calculation change if Amanda and Charlene contributed a different amount?
2. How could you set up this problem if Brandon’s share was known?
3. How does the method change when working with different ratios?
4. What happens if all three gave the same amount?
5. How would you approach this if only Amanda’s contribution was known?

Tip: When dealing with ratios, always try to express everything in terms of one variable for easier calculations.