Final answer:
To determine the area of each room, the total area of 360 square feet is divided by the sum of the parts of the ratio (12) to find the area per part (30 square feet). The living room (150 square feet) is thus found to be 30 square feet larger than the bedroom (120 square feet).
Step-by-step explanation:
The student's question relates to the area of the rooms in a house, specifically the ratio of these areas and the difference in size between the living room and the bedroom. Given the ratio of the area of the living room to the kitchen to the bedroom as 5:3:4, and the combined area of those three rooms as 360 square feet, we can calculate the individual areas.
First, we find the sum of the parts of the ratio, which is 5 + 3 + 4 = 12 parts. Then, we determine the size of one part by dividing the total combined area by the number of parts:
360 square feet ÷ 12 parts = 30 square feet per part.
Now, we can calculate the area of each room:
- Living room: 5 parts × 30 square feet per part = 150 square feet
- Kitchen: 3 parts × 30 square feet per part = 90 square feet
- Bedroom: 4 parts × 30 square feet per part = 120 square feet
To find out how much larger the living room is than the bedroom, we subtract the area of the bedroom from the area of the living room:
150 square feet (living room) - 120 square feet (bedroom) = 30 square feet.
Therefore, the living room is 30 square feet larger than the bedroom.