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 the difference between the number of laptops sold by store D and E is 75% less than the number of laptops sold by store F and the ratio between the number of laptops sold by store F and the number of laptops unsold by the same store is $62 : 75$, then find out the number of laptops unsold by store F.

### Concept & Ratio Applications By finding the exact number of laptops sold by Store D and E from the pie chart variables, we can use the given percentages and ratios to find unknown values for an external Store F. ### Step-by-Step Solution * **Given:** $z = 14$ and $y = 56$ (solved from base conditions). Store D = $(2z - 5)\% = 23\%$. Store E = $(8.5z + 1)^\circ = 120^\circ$. * **Calculation:** Total laptops = 7200. * Store D laptops = $0.23 \times 7200 = 1656$. * Store E laptops = $\frac{120}{360} \times 7200 = 2400$. * **Deduction:** Difference between D and E = $2400 - 1656 = 744$. * This difference is 75% less than laptops sold by store F ($S_F$). Thus, it represents 25% (or $\frac{1}{4}$) of $S_F$. * $744 = 0.25 \times S_F \implies S_F = 744 \times 4 = 2976$. * The ratio of sold to unsold ($U_F$) by store F is 62:75. * $\frac{2976}{U_F} = \frac{62}{75} \implies U_F = \frac{2976 \times 75}{62}$. * $U_F = 48 \times 75 = 3600$. ### Exam Strategy & Shortcut Recognize that "75% less than" means exactly 25% or $\frac{1}{4}$ of the value. Multiplying the difference 744 by 4 quickly gives the sold units. For the ratio, directly scaling up 62 to 2976 (a multiplier of 48) allows you to just multiply 75 by 48 (which is $75 \times 50 - 75 \times 2 = 3750 - 150 = 3600$) to find the unsold units mentally. ### Common Pitfall A common pitfall is calculating 75% of 744 rather than correctly setting 744 as the 25% remainder of the unknown total. ### Final Answer Therefore, the correct answer is **3600**.