1. **Problem 16:** Thomas's monthly salary $S$ is a linear function of the number of tablets sold $n$. Given points: $(6, 8160)$ and $(13, 12080)$. Find $S$ when $n=18$ and check if $S=22600$ is possible. 2. **Formula:** For a linear function $S = mn + c$, where $m$ is the slope and $c$ is the intercept. 3. **Find slope $m$:** $$m = \frac{12080 - 8160}{13 - 6} = \frac{3920}{7} = 560$$ 4. **Find intercept $c$:** Using point $(6, 8160)$, $$8160 = 560 \times 6 + c \Rightarrow c = 8160 - 3360 = 4800$$ 5. **Linear function:** $$S = 560n + 4800$$ 6. **(a) Find $S$ when $n=18$:** $$S = 560 \times 18 + 4800 = 10080 + 4800 = 14880$$ 7. **(b) Check if $S=22600$ is possible:** Solve for $n$: $$22600 = 560n + 4800 \Rightarrow 560n = 17800 \Rightarrow n = \frac{17800}{560} = 31.7857...$$ Since $n$ must be an integer number of tablets sold, $31.7857$ is not possible. So, no, $S=22600$ is not possible for an integer $n$. 8. **Problem 17:** Given $f(x) = ax + k$ and $g(x) = bx + k$ with $a > b > 0$. 9. **(a)(i) Find $f(4) - g(4)$:** $$f(4) - g(4) = (a \times 4 + k) - (b \times 4 + k) = 4a + k - 4b - k = 4(a - b)$$ 10. **(a)(ii) Find $f(6) - g(6)$:** $$f(6) - g(6) = (a \times 6 + k) - (b \times 6 + k) = 6a + k - 6b - k = 6(a - b)$$ **Summary:** - Thomas's salary function: $S = 560n + 4800$ - Salary at $n=18$ is $14880$ - Salary $22600$ is not possible for integer $n$ - Differences: $f(4)-g(4) = 4(a-b)$ and $f(6)-g(6) = 6(a-b)$