Question 291640: You Are planning to rebuild your garage, which currently measure 20 feet by 30 feet. You want the new garage to be larger than the existing one, but in the same proportions as the original. If you increase the width by x feet, you will have to increase the length by (3/2)*x feet. Write the floor area of the new garage in terms of the variable x.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! The floor area of the original garage is equal to:
y = 30 * 20
The length is 30 feet.
The width is 20 feet.
The area is equal to the length times the width.
If you want to increase the width by x feet, then you have to increase the length by (3/2)x feet.
Your general equation will be:
y = (30 + (3/2)x) * (20 + x)
When x = 0, this reduces to y = 30 * 20 which is the original square feet of the garage.
Simplify this equation to get:
y = (30*20) + 30*x + 30*x + (3/2)*x*x which becomes:
y = 600 + 60x + (3/2)x^2.
For example:
If you wish to increase the width of the garage by 10 feet, this means that x = 10.
Your new area will be 600 + 600 + 150 = 1350 square feet.
When x = 10, (3/2)x = 15.
Since your original width was 20, your new width is 30.
Since your original length was 30, your new length is 45.
Your new area is 30 * 45 = 1350 square feet.
The equation is good.
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