Question 1

Explanation

Given the operation $\triangle(a, b) = ka + \frac{b}{m}$ where $k$ and $m$ are positive integers.

From $\triangle(2, 4) = 8$, we get

Multiply both sides by $m$

From $\triangle(3, 5) = 11$, we get

Multiply both sides by $m$

Eliminate $km$ by multiplying equation $\text{(1)}$ by $3$ and equation $\text{(2)}$ by $2$

Subtract equation $\text{(2a)}$ from equation $\text{(1a)}$

Substitute $m = 1$ into equation $\text{(1)}$

With $k = 2$ and $m = 1$, the value of $\triangle(5, 9)$ is