SOLUTION: A photograph is 8in by 10in. A. Write an equation to find the amount x that should be added to the current length and width to double the area of the photograph. B. Solve the e

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A photograph is 8in by 10in. A. Write an equation to find the amount x that should be added to the current length and width to double the area of the photograph. B. Solve the e      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 588867: A photograph is 8in by 10in.
A. Write an equation to find the amount x that should be added to the current length and width to double the area of the photograph.
B. Solve the equation.
C. What will the new dimensions be?
Thank you soo much if you answer this.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The original area is 8*10 = 80 square inches.

The doubled area is 80*2 = 160 square inches.

The new dimensions are 8+x by 10+x and they multiply out to 160, so the equation is (8+x)(10+x) = 160
-------------------------------------------------------
b)

Now get the equation into standard form

(8+x)(10+x) = 160

80+18x+x^2 = 160

80+18x+x^2 - 160 = 0

x^2 + 18x - 80 = 0

Now use the quadratic formula to solve for x

x = (-b+-sqrt(b^2-4ac))/(2a)

x = (-(18)+-sqrt((18)^2-4(1)(-80)))/(2(1))

x = (-18+-sqrt(324-(-320)))/(2)

x = (-18+-sqrt(644))/2

x = (-18+sqrt(644))/2 or x = (-18-sqrt(644))/2

x = (-18+2*sqrt(161))/2 or x = (-18-2*sqrt(161))/2

and approximate the solutions above to get

x = 3.6885775 or x = -21.6885775

toss out the negative solution to get

x = 3.6885775

So you should add about 3.6885775 inches to each dimension to double the area of the photograph.

-------------------------------------------------------
C)
Add 8 and 3.6885775 to get 11.6885775. This is the new width

Add 10 and 3.6885775 to get 13.6885775. This is the new length