The office and the living room in a tiny house share a wall. The area of the office is 18 square feet. The area of the living room is 48 square feet. The expression 18 48 represents the total area in square feet. Which of the following expressions also show the total area of the two rooms? Choose all that apply
The correct answer and explanation is:
To find the total area of the office and the living room, you simply add their individual areas:
- Area of office = 18 square feet
- Area of living room = 48 square feet
- Total area = 18 + 48
So, the expression 18 + 48 represents the total area.
Other expressions that show the total area:
We are asked to find all the expressions that also show the total area. Let’s look at other possible correct options using basic math:
- 48 + 18 – ✅ Yes. Addition is commutative, meaning the order doesn’t matter: 18+48=66and48+18=6618 + 48 = 66 \quad \text{and} \quad 48 + 18 = 66
- (20 – 2) + (50 – 2) – ✅ Let’s simplify: (20–2)=18and(50–2)=48⇒18+48=66(20 – 2) = 18 \quad \text{and} \quad (50 – 2) = 48 \Rightarrow 18 + 48 = 66 This is another valid way to represent the total.
- 66 – ✅ Yes. This is the actual total area as a single number, rather than an expression, but still represents the correct total.
- (10 + 8) + (40 + 8) – ✅ Simplify: 10+8=18and40+8=48⇒18+48=6610 + 8 = 18 \quad \text{and} \quad 40 + 8 = 48 \Rightarrow 18 + 48 = 66
Incorrect options (if presented):
- 18 × 48 – ❌ This gives 864, which is not a total area of two rooms.
- 48 – 18 – ❌ This gives 30, which is not a total area.
- 18 ÷ 48 – ❌ This is a ratio, not a total area.
Summary:
Correct expressions that represent the total area of the two rooms are:
✅ 18 + 48
✅ 48 + 18
✅ (20 – 2) + (50 – 2)
✅ (10 + 8) + (40 + 8)
✅ 66
These all simplify to the same total: 66 square feet.