1. **Problem:** Lori owes her mother 39. She pays back 1/3 of this debt, then 1/4 of the remaining debt. How much does she still owe? 2. **Formula and rules:** To find the remaining debt after partial payments, subtract the paid amounts stepwise from the original debt. 3. **Step 1:** Calculate 1/3 of 39: $$\frac{1}{3} \times 39 = 13$$ 4. **Step 2:** Remaining debt after first payment: $$39 - 13 = 26$$ 5. **Step 3:** Calculate 1/4 of remaining debt: $$\frac{1}{4} \times 26 = 6.5$$ 6. **Step 4:** Remaining debt after second payment: $$26 - 6.5 = 19.5$$ 7. **Answer:** Lori still owes her mother 19.5. --- 1. **Problem:** A recipe calls for 2/3 cup of butter. If quadrupled, express the amount as (a) an improper fraction and (b) a mixed number. 2. **Formula:** Multiply the original amount by 4. 3. **Calculation:** $$4 \times \frac{2}{3} = \frac{8}{3}$$ 4. **(a) Improper fraction:** $$\frac{8}{3}$$ 5. **(b) Mixed number:** Divide 8 by 3: quotient 2, remainder 2, so $$2 \frac{2}{3}$$ --- 1. **Problem:** A carpenter has 64 feet of baseboard. He installs 1/2 in one room, then 3/4 of the remainder in another. How much is left? 2. **Step 1:** Installed in first room: $$\frac{1}{2} \times 64 = 32$$ 3. **Step 2:** Remaining after first room: $$64 - 32 = 32$$ 4. **Step 3:** Installed in second room: $$\frac{3}{4} \times 32 = 24$$ 5. **Step 4:** Remaining after second room: $$32 - 24 = 8$$ 6. **Answer:** 8 feet of baseboard remain. --- 1. **Problem:** Time zones relative to London. Given times for various locations. 2. **(a) Hours St. John's ahead of Brandon:** St. John's: $$-3 \frac{1}{2} = -3.5$$ Brandon: $$-6$$ Difference: $$-3.5 - (-6) = 2.5$$ hours ahead. 3. **(b) Hours Victoria behind Mumbai:** Victoria: $$-8$$ Mumbai: $$+5 \frac{1}{2} = 5.5$$ Difference: $$-8 - 5.5 = -13.5$$, so Victoria is 13.5 hours behind Mumbai. 4. **(c) Which location experiences sunrise first, Istanbul or St. John's?** Istanbul: +2 hours St. John's: -3.5 hours Since Istanbul is ahead of London by 2 hours and St. John's is behind by 3.5 hours, Istanbul experiences sunrise first. 5. **(d) Location halfway between Istanbul (+2) and Alice Springs (+9 \frac{1}{2} = 9.5):** Midpoint: $$\frac{2 + 9.5}{2} = \frac{11.5}{2} = 5.75$$ Closest time zone: Kathmandu (+5 \frac{3}{4} = 5.75) 6. **(e) If time is 3:30 p.m. in London, time in Victoria (-8):** Subtract 8 hours: $$3:30 \text{ p.m.} - 8 \text{ hours} = 7:30 \text{ a.m.}$$ --- **Final answers:** 1) 19.5 2a) $$\frac{8}{3}$$ 2b) $$2 \frac{2}{3}$$ 3) 8 4a) 2.5 hours 4b) 13.5 hours 4c) Istanbul 4d) Kathmandu 4e) 7:30 a.m.