Subjects arithmetic, geometry

Sugar Pies Angle B00611

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1. **Problem 35:** Carla used 6 \frac{1}{2} cups of sugar to make 5 pies. How many cups of sugar will she need to make 2 pies? 2. **Step 1:** Convert mixed number to improper fraction: $$6 \frac{1}{2} = \frac{13}{2}$$ 3. **Step 2:** Find sugar per pie by dividing total sugar by number of pies: $$\frac{13}{2} \div 5 = \frac{13}{2} \times \frac{1}{5} = \frac{13}{10}$$ 4. **Step 3:** Calculate sugar needed for 2 pies: $$\frac{13}{10} \times 2 = \frac{26}{10} = \frac{13}{5}$$ 5. **Step 4:** Convert improper fraction to mixed number: $$\frac{13}{5} = 2 \frac{3}{5}$$ 6. **Answer for 35:** 2 \frac{3}{5} cups (Option B) 7. **Problem 37:** Given angles on a straight line: left angle = 7x, middle shaded angle = 8x, right angle = 44.4°. 8. **Step 1:** Sum of angles on a straight line is 180°: $$7x + 8x + 44.4 = 180$$ 9. **Step 2:** Combine like terms: $$15x + 44.4 = 180$$ 10. **Step 3:** Subtract 44.4 from both sides: $$15x = 180 - 44.4 = 135.6$$ 11. **Step 4:** Solve for x: $$x = \frac{135.6}{15}$$ $$x = 9.04$$ 12. **Step 5:** Find shaded angle (8x): $$8 \times 9.04 = 72.32^{\circ}$$ 13. **Answer for 37:** The shaded angle measures approximately 72.32°
35. Sugar Pies37. Angle7x8x44.4°