Sofea bought $(8x + 14)$ textbooks with each textbook costing RM$5x$. She paid RM300 for all the textbooks she bought. We need to find the number of textbooks Sofea bought, which is the value of the expression $(8x+14)$.

1. Problem Description

Sofea bought $(8x + 14)$ textbooks with each textbook costing RM$5x$. She paid RM300 for all the textbooks she bought. We need to find the number of textbooks Sofea bought, which is the value of the expression $(8x+14)$.

2. Solution Steps

The total cost of the textbooks is the number of textbooks multiplied by the price per textbook. We are given that the total cost is RM

3

0

0. Therefore, we can write the equation:

$(8x + 14) \times (5x) = 300$

Expanding the left side, we get:

$40x^2 + 70x = 300$

Dividing the entire equation by 10, we get:

$4x^2 + 7x = 30$

Rearranging the equation to form a quadratic equation:

$4x^2 + 7x - 30 = 0$

We need to factorize this quadratic equation. We are looking for two numbers that multiply to $4 \times -30 = -120$ and add up to $7$. These numbers are $15$ and $-8$.

We rewrite the middle term $7x$ as $15x - 8x$:

$4x^2 + 15x - 8x - 30 = 0$

Now, factor by grouping:

$x(4x + 15) - 2(4x + 15) = 0$

$(x - 2)(4x + 15) = 0$

This gives us two possible solutions for $x$:

$x - 2 = 0$ or $4x + 15 = 0$

$x = 2$ or $x = -\frac{15}{4}$

Since the price of the textbooks, $5x$, must be positive, $x$ must be positive. Therefore, we have $x=2$.

Now, we can find the number of textbooks Sofea bought, which is $(8x + 14)$.

Number of textbooks $= 8x + 14 = 8(2) + 14 = 16 + 14 = 30$.

3. Final Answer

30