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The area of a rectangular kitchen is 80 square feet. If the length of the floor is 4 feet less than four times the width. what is the width of the floor in feet?
- a)4
- b)5
- c)8
- d)16
- e)17
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The area of a rectangular kitchen is 80 square feet. If the length of ...
Problem:
The area of a rectangular kitchen is 80 square feet. If the length of the floor is 4 feet less than four times the width, what is the width of the floor in feet?
Solution:
Let's assume the width of the floor is 'x' feet.
Step 1: Find the equation representing the given information.
According to the problem statement, the length of the floor is 4 feet less than four times the width. So, the length can be represented as (4x - 4) feet.
The area of a rectangle is given by the formula: Area = Length * Width.
We are given that the area of the rectangular kitchen is 80 square feet. So, we can write the equation as:
80 = (4x - 4) * x
Step 2: Solve the equation for 'x'.
To solve the equation, we need to simplify and rearrange it.
80 = (4x - 4) * x
80 = 4x^2 - 4x
4x^2 - 4x - 80 = 0
Step 3: Factor or use the quadratic formula to solve the equation.
To factor the quadratic equation, we can first divide the equation by 4 to simplify it:
x^2 - x - 20 = 0
Now, we need to find two numbers whose product is -20 and whose sum is -1 (the coefficient of 'x'). The numbers are -5 and 4.
So, we can factor the equation as:
(x - 5)(x + 4) = 0
Setting each factor equal to zero, we get:
x - 5 = 0 or x + 4 = 0
x = 5 or x = -4
Step 4: Determine the valid solution.
Since the width of the floor cannot be negative, we can discard the solution x = -4.
Therefore, the width of the floor is x = 5 feet.
Thus, the correct answer is option 'B' (5).
The area of a rectangular kitchen is 80 square feet. If the length of the floor is 4 feet less than four times the width, what is the width of the floor in feet?
Solution:
Let's assume the width of the floor is 'x' feet.
Step 1: Find the equation representing the given information.
According to the problem statement, the length of the floor is 4 feet less than four times the width. So, the length can be represented as (4x - 4) feet.
The area of a rectangle is given by the formula: Area = Length * Width.
We are given that the area of the rectangular kitchen is 80 square feet. So, we can write the equation as:
80 = (4x - 4) * x
Step 2: Solve the equation for 'x'.
To solve the equation, we need to simplify and rearrange it.
80 = (4x - 4) * x
80 = 4x^2 - 4x
4x^2 - 4x - 80 = 0
Step 3: Factor or use the quadratic formula to solve the equation.
To factor the quadratic equation, we can first divide the equation by 4 to simplify it:
x^2 - x - 20 = 0
Now, we need to find two numbers whose product is -20 and whose sum is -1 (the coefficient of 'x'). The numbers are -5 and 4.
So, we can factor the equation as:
(x - 5)(x + 4) = 0
Setting each factor equal to zero, we get:
x - 5 = 0 or x + 4 = 0
x = 5 or x = -4
Step 4: Determine the valid solution.
Since the width of the floor cannot be negative, we can discard the solution x = -4.
Therefore, the width of the floor is x = 5 feet.
Thus, the correct answer is option 'B' (5).
Community Answer
The area of a rectangular kitchen is 80 square feet. If the length of ...
The area of a rectangle is calculated by multiplying the width by the length (w × l). You are given that the length is 4 feet less than four times the width. Set the width equal to w; the length is then 4w − 4. Plug these values into the equation for the area of a rectangle:
(w)(4w − 4) = 80
4w2 − 4w = 80
Put this equation into the quadratic form and factor to find the solutions for w:
4w2 − 4w − 80 = 0
4(w2 − w − 20) = 0
4(w + ___)(w − ___) = 0
4(w + 4)(w − 5) = 0
(w + 4) = 0; w = −4
(w − 5) = 0; w = 5
Since the width of a room cannot have a negative value, the width must be 5.
(w)(4w − 4) = 80
4w2 − 4w = 80
Put this equation into the quadratic form and factor to find the solutions for w:
4w2 − 4w − 80 = 0
4(w2 − w − 20) = 0
4(w + ___)(w − ___) = 0
4(w + 4)(w − 5) = 0
(w + 4) = 0; w = −4
(w − 5) = 0; w = 5
Since the width of a room cannot have a negative value, the width must be 5.
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The area of a rectangular kitchen is 80 square feet. If the length of the floor is 4 feet less than four times the width. what is the width of the floor in feet?a)4b)5c)8d)16e)17Correct answer is option 'B'. Can you explain this answer?
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