1. **Stating the problem:** We are given that $A$ is partly constant and partly varies with $x$. We have values: when $x=16$, $A=13$; when $x=24$, $A=13$; and when $x=24$, $A=17$. There seems to be a contradiction in the values for $x=24$, so we will clarify the problem assuming the last value is correct and the second is a typo. 2. **Understanding the relationship:** If $A$ is partly constant and partly varies with $x$, we can express $A$ as: $$A = k + m x$$ where $k$ is the constant part and $m x$ is the part that varies with $x$. 3. **Using the given points:** Using the points $(16,13)$ and $(24,17)$: $$13 = k + 16m$$ $$17 = k + 24m$$ 4. **Solving the system:** Subtract the first equation from the second: $$17 - 13 = (k + 24m) - (k + 16m)$$ $$4 = 8m$$ $$m = \frac{4}{8} = 0.5$$ 5. **Finding $k$:** Substitute $m=0.5$ into the first equation: $$13 = k + 16 \times 0.5$$ $$13 = k + 8$$ $$k = 13 - 8 = 5$$ 6. **Final formula:** $$A = 5 + 0.5 x$$ This formula shows $A$ has a constant part 5 and varies linearly with $x$ with a coefficient 0.5. **Answer:** $A = 5 + 0.5 x$