Solving word problem using quadratic equation.
The book says the answer is 20 feet. I know how to solve the equation. I do not know where the 20 feet is coming from.
Problem:
Mr. Ingram wants to add a garage to his home. The dimensions of his home are 50ft by 20ft. When securing his buisling permit, he found that his home with the garage cannot be more then 1,400 square feet. How long can he extend the side of his house that is 50ft. long so that his remoding project will follow the code?
Using FOIL:
(X+50) (X+20) = 1,400
X^2+75X-400=0
(X-5) (X+80)
X=5
X=-80
The answer I get is the 5 ft. Where is the 20 feet coming from?
It is easier than you made it
You said <How long can he extend the side of his house that is 50ft. long..> so only the length is to be extended.
then 20(x+50) = 1400
20x + 1000 = 1400
20x = 400
x = 20
Only toe 50 ft. side is being increased.
Therefore, 20(x + 50) = 1400 or
20x + 1000 = 1400 or 20x = 400 making x = 20 ft.
Wow, 3 postings in a row where we were just minutes apart, and almost identical solutions.
Who said great minds don't think alike, lol
To solve this problem, we can represent the dimensions of the extended side of the house as 'x.' Since the original dimension is 50ft, we can add 'x' to it to find the extended length of the side. The length of the other side is fixed at 20ft.
With this information, we can write the equation for the area of the house plus the garage:
(x+50) * 20 = 1,400
Now, let's solve this equation step by step:
1. Distribute the 20 to both terms inside the parentheses:
20x + 1000 = 1,400
2. Move 1000 to the other side of the equation:
20x = 1,400 - 1000
20x = 400
3. Divide both sides by 20 to isolate 'x':
x = 400 / 20
x = 20
So, according to the quadratic equation solution, the extended length of the side of the house should be 20ft. The answer of 5ft might have come from a mistake or miscalculation in the previous steps of solving the quadratic equation.