The price of one kaya bun is RMx and the price
of one butter bun is RMy. Suzi buys 6 kaya
buns and 3 butter buns while Fauzi buys 4 kaya
buns and 5 butter buns. Suzi pays RM8.40 and
Fauzi pays RM1 less than Suzi. Using the matrix
method, calculate the price of one kaya bun and
the price of one butter bun.

Question

UpStudy AI · Accepted Answer

To determine the prices of one kaya bun (**RMx**) and one butter bun (**RMy**), we can set up a system of linear equations based on the purchases made by Suzi and Fauzi. We'll then solve this system using the matrix method.

### Step 1: Formulate the Equations

From the problem:

1. **Suzi's Purchase:**
   $$
   6x + 3y = 8.40
   $$
   
2. **Fauzi's Purchase:**
   $$
   4x + 5y = 7.40
   $$
   *(Note: Fauzi pays RM1 less than Suzi, so $$8.40 - 1 = 7.40$$)*

### Step 2: Represent as a Matrix Equation

The system can be written in matrix form as:
$$
\begin{bmatrix}
6 & 3 \
4 & 5 \
\end{bmatrix}
\begin{bmatrix}
x \
y \
\end{bmatrix}
=
\begin{bmatrix}
8.40 \
7.40 \
\end{bmatrix}
$$

### Step 3: Find the Inverse of the Coefficient Matrix

Let $$ A = \begin{bmatrix} 6 & 3 \ 4 & 5 \end{bmatrix} $$ and $$ \mathbf{b} = \begin{bmatrix} 8.40 \ 7.40 \end{bmatrix} $$.

First, compute the determinant of $$ A $$:
$$
\text{det}(A) = (6)(5) - (4)(3) = 30 - 12 = 18
$$

The inverse of $$ A $$ is:
$$
A^{-1} = \frac{1}{\text{det}(A)} \begin{bmatrix} 5 & -3 \ -4 & 6 \end{bmatrix} = \frac{1}{18} \begin{bmatrix} 5 & -3 \ -4 & 6 \end{bmatrix}
$$

### Step 4: Multiply the Inverse by Vector $$ \mathbf{b} $$

$$
\begin{bmatrix}
x \
y \
\end{bmatrix}
= A^{-1} \mathbf{b}
= \frac{1}{18} \begin{bmatrix} 5 & -3 \ -4 & 6 \end{bmatrix} \begin{bmatrix} 8.40 \ 7.40 \end{bmatrix}
$$

Calculating the products:
$$
x = \frac{1}{18} (5 \times 8.40 - 3 \times 7.40) = \frac{1}{18} (42.00 - 22.20) = \frac{19.80}{18} = 1.10
$$
$$
y = \frac{1}{18} (-4 \times 8.40 + 6 \times 7.40) = \frac{1}{18} (-33.60 + 44.40) = \frac{10.80}{18} = 0.60
$$

### Conclusion

- **Price of one kaya bun (x):** RM **1.10**
- **Price of one butter bun (y):** RM **0.60**

**Answer:**  
One kaya bun costs RM 1.10 and one butter bun costs RM 0.60.
One kaya bun costs RM 1.10 and one butter bun costs RM 0.60.

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

[

Now we multiply this inverse matrix by the constants matrix:
[

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