1. Problem 6: Find the total amount of money raised by the three groups (adults, parents, and eighth-grade class). Given: - Adults raised 700 - Total raised was 2400 - Adults and eighth-grade class together raised 1625 Step 1: Let $P$ be the amount raised by parents, and $E$ be the amount raised by the eighth-grade class. Step 2: From the problem, we have: $$700 + P + E = 2400$$ $$700 + E = 1625$$ Step 3: Solve for $E$: $$E = 1625 - 700 = 925$$ Step 4: Substitute $E$ back into the total: $$700 + P + 925 = 2400$$ $$P = 2400 - 700 - 925 = 775$$ Step 5: Total amount raised by the three groups is the total given: $$\boxed{2400}$$ --- 2. Problem 7: Find how many votes Scott received. Given: - Yuan received 45% of the votes - Scott received 18 more votes than Yuan Step 1: Let $V$ be the total number of votes. Step 2: Yuan's votes: $$0.45V$$ Step 3: Scott's votes: $$0.45V + 18$$ Step 4: Since Yuan and Scott are the only candidates, their votes sum to total votes: $$0.45V + (0.45V + 18) = V$$ Step 5: Simplify and solve for $V$: $$0.9V + 18 = V$$ $$18 = V - 0.9V = 0.1V$$ $$V = \frac{18}{0.1} = 180$$ Step 6: Scott's votes: $$0.45 \times 180 + 18 = 81 + 18 = 99$$ Step 7: Final answer: $$\boxed{99}$$ --- 3. Problem 8: Find the total amount of money the team needs to raise. Given: - Raised 5500, which is 65% of total needed Step 1: Let $T$ be the total amount needed. Step 2: Write the equation: $$0.65T = 5500$$ Step 3: Solve for $T$: $$T = \frac{5500}{0.65} = 8461.54$$ Step 4: The team needs to raise: $$\boxed{8461.54}$$