1. **State the problem:** We have numbers 1, 27, 35, 44, 52 corresponding to 172, and we want to find the scaled numbers corresponding to 194 using a scaling factor. 2. **Formula used:** To scale numbers proportionally, use the formula: $$\text{new number} = \text{old number} \times \frac{\text{new total}}{\text{old total}}$$ 3. **Calculate the scaling factor:** $$\text{scaling factor} = \frac{194}{172}$$ 4. **Apply the scaling factor to each number:** - For 1: $$1 \times \frac{194}{172} = \frac{194}{172}$$ - For 27: $$27 \times \frac{194}{172} = \frac{27 \times 194}{172}$$ - For 35: $$35 \times \frac{194}{172} = \frac{35 \times 194}{172}$$ - For 44: $$44 \times \frac{194}{172} = \frac{44 \times 194}{172}$$ - For 52: $$52 \times \frac{194}{172} = \frac{52 \times 194}{172}$$ 5. **Simplify each scaled number:** - $$\frac{194}{172} = \frac{97}{86} \approx 1.128$$ - $$27 \times \frac{194}{172} = 27 \times 1.128 \approx 30.46$$ - $$35 \times \frac{194}{172} = 35 \times 1.128 \approx 39.48$$ - $$44 \times \frac{194}{172} = 44 \times 1.128 \approx 49.63$$ - $$52 \times \frac{194}{172} = 52 \times 1.128 \approx 58.66$$ 6. **Final scaled numbers:** $$\boxed{1.13, 30.46, 39.48, 49.63, 58.66}$$ These are the numbers scaled from total 172 to total 194.