Direction: Study the following information carefully and answer the questions. The following pie chart shows the distribution of the number of laptops sold by five stores. Conditions: I. The total number of laptops sold by all the five stores (A, B, C, D and E) taken together is 7200. II. $(19z - 4y) = 42$ III. $z^2 + 2z - 224 = 0$ Note: The values given in the above given pie chart in the form of degree or percentage form cannot be negative. If 38% of the all laptops sold by store E are gaming laptops and remaining are non gaming laptops, then find out the number of non gaming laptops sold by store E.

### Concept & Data Interpretation To evaluate specific segments of the pie chart, we must first determine the variables $z$ and $y$ by solving the algebraic equations provided in the conditions, which will then unlock the exact number of laptops sold by Store E. ### Step-by-Step Solution * **Given:** Condition III states $z^2 + 2z - 224 = 0$. * **Calculate $z$:** Factoring the quadratic equation gives $(z + 16)(z - 14) = 0$. Since pie chart percentages/degrees cannot be negative (Store D is $(2z - 5)\%$), $z$ must be $14$. * **Calculate $y$:** Substitute $z = 14$ into Condition II: $19(14) - 4y = 42 \implies 266 - 4y = 42 \implies 4y = 224 \implies y = 56$. * **Calculate Store E total:** Store E is $(8.5z + 1)^\circ$. Substituting $z = 14$, we get $(8.5(14) + 1)^\circ = (119 + 1)^\circ = 120^\circ$. * Total laptops are 7200, which corresponds to $360^\circ$. Thus, Store E's share is $\frac{120}{360} \times 7200 = 2400$ laptops. * **Calculate non-gaming laptops:** 38% are gaming, meaning the remaining $100\% - 38\% = 62\%$ are non-gaming. * Number of non-gaming laptops = $62\%$ of $2400 = 0.62 \times 2400 = 1488$. ### Exam Strategy & Shortcut When you discover Store E's sector is $120^\circ$, immediately recognize that it represents exactly $\frac{1}{3}$ of the entire circle. Finding $\frac{1}{3}$ of 7200 instantly gives 2400. From there, computing $62\%$ directly (rather than finding $38\%$ and subtracting) saves valuable calculation time. ### Common Pitfall A common mistake is failing to convert the degrees ($120^\circ$) to a percentage or raw value relative to the $360^\circ$ circle, which results in incorrect total base values for Store E. ### Final Answer Therefore, the correct answer is **1488**.