When Marcus wakes up, his house is 40 degrees. He spends 3 hours baking, and every hour the oven is on it raises the house's temperature by 5 degrees. Then Marcus opens a window for 30 minutes, and the house cools down 2 degrees for every 10 minutes the window is open. What is the house's final temperature?
Get the complete, step-by-step math solution for: "When Marcus wakes up, his house is 40 degrees. He spends 3 hours baking, and every hour the oven is on it raises the house's temperature by 5 degrees....". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Initial Temperature
Start with the initial temperature of the house when Marcus wakes up. This is given as 40∘.
Step 2: Temperature increase from baking
Calculate the total temperature increase due to baking. Marcus bakes for 3 hours, and the oven raises the temperature by 5∘ each hour.
Step 3: Calculate increase from baking
Multiply the number of hours by the temperature increase per hour to find the total increase. So, 3×5=15∘.
Step 4: Temperature after baking
Add the temperature increase from baking to the initial temperature to find the house's temperature after baking.
Step 5: Calculate temperature after baking
Perform the addition: 40+15=55∘. This is the temperature of the house before the window is opened.
Step 6: Cooling intervals from window
Determine how many 10-minute cooling intervals are in the 30 minutes the window is open. Each interval causes a 2∘ drop.
Step 7: Calculate number of cooling intervals
Divide the total time the window is open by the duration of each cooling interval to find the number of times the temperature drops.
Step 8: Total temperature decrease from window
Calculate the total temperature decrease from the window being open. Each interval reduces the temperature by 2∘.
Step 9: Calculate total decrease from window
Multiply the number of cooling intervals by the temperature drop per interval: 3×2=6∘.
Step 10: Final Temperature
Subtract the total temperature decrease from the temperature after baking to find the house's final temperature.
Step 11: Calculate final temperature
Perform the final subtraction: 55−6=49∘. This is the final temperature of the house.