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?



We are given the ratios of how Amanda, Brandon, and Charlene shared the cost of a present, and we know the total contribution of Amanda and Charlene. Let's denote their contributions as follows:

- Let Amanda's share be \( A \),
- Brandon's share be \( B \),
- Charlene's share be \( C \).

We are given two ratios:

1. \( \frac{A}{B} = \frac{4}{5} \), which means Amanda's share is 4 parts for every 5 parts of Brandon's share.
2. \( \frac{B}{C} = \frac{2}{3} \), which means Brandon's share is 2 parts for every 3 parts of Charlene's share.

Additionally, we know that Amanda and Charlene together contributed R46:
\[
A + C = 46
\]

### Step 1: Express shares in terms of a common variable
We first express all shares in terms of a common variable. From the ratio \( \frac{A}{B} = \frac{4}{5} \), we can express \( A \) and \( B \) in terms of a variable \( x \):
\[
A = 4x, \quad B = 5x
\]

From the ratio \( \frac{B}{C} = \frac{2}{3} \), we can express \( B \) and \( C \) in terms of another variable \( y \):
\[
B = 2y, \quad C = 3y
\]

### Step 2: Relate the two expressions for \( B \)
We now have two expressions for \( B \): one from the first ratio and another from the second ratio:
\[
5x = 2y
\]
Solve for \( y \) in terms of \( x \):
\[
y = \frac{5x}{2}
\]

### Step 3: Substitute \( y \) into the equation for \( C \)
Now substitute \( y = \frac{5x}{2} \) into the expression for \( C \):
\[
C = 3y = 3 \times \frac{5x}{2} = \frac{15x}{2}
\]

### Step 4: Use the total contribution of Amanda and Charlene
We know that Amanda and Charlene's combined contribution is R46:
\[
A + C = 46
\]
Substitute \( A = 4x \) and \( C = \frac{15x}{2} \) into this equation:
\[
4x + \frac{15x}{2} = 46
\]
Multiply through by 2 to eliminate the fraction:
\[
8x + 15x = 92
\]
Combine like terms:
\[
23x = 92
\]
Solve for \( x \):
\[
x = \frac{92}{23} = 4
\]

### Step 5: Find the total cost of the present
Now that we have \( x = 4 \), we can find the shares of Amanda, Brandon, and Charlene:
- \( A = 4x = 4 \times 4 = 16 \),
- \( B = 5x = 5 \times 4 = 20 \),
- \( C = \frac{15x}{2} = \frac{15 \times 4}{2} = 30 \).

The total cost of the present is the sum of their contributions:
\[
A + B + C = 16 + 20 + 30 = 66
\]

Thus, the total cost of the present is **R66**.

Would you like a more detailed explanation of any step, or do you have any questions?

Here are five related questions to consider:

1. If the total contribution was R92 instead of R46, what would be the new total cost of the present?
2. How would the problem change if Amanda and Charlene gave a total of R60 for the present?
3. If the ratio between Amanda's and Brandon's share was 5:6, how would the calculations change?
4. What if Charlene's contribution was doubled—how would that affect the total cost?
5. How would the solution differ if all three contributed equally?

**Tip:** Always check if the sum of individual shares adds up correctly to the total cost when dealing with ratios.

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?

Explore how Amanda, Brandon, and Charlene shared the cost of a present using ratio concepts. Amanda's and Charlene's total contribution was R46, and we calculate the total cost of the present step by step. Suitable for Grades 8-10, this problem covers ratios and linear equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation