What is the value of "x"?

Question

The dimensions of an old stage are 30 feet wide and 15 feet deep. The new stage is 1000 square feet. The demensions of the new stage were created by adding "x" to the width and the depth of the old stage demensions. 

Answer 1

• (x+30)(x+15)=1000 ~ A=wl
• x²+45x+450=100 ~ FOIL/distribute
• x²+45x-550=0 ~ Set equal to zero
• (x+55)(x-10)=0 ~ Refactor
• x=10 or -55 ~ mathematical answers
• x=10 (x can't be negative for this problem)

Answer 2

The area of the new stage is (x + 30)(x + 15), So

 

(x + 30)(x + 15) = 1000

 

x² + 30x + 15x + 450 = 1000

 

x² + 45x + 450 = 1000

 

x² + 45x - 550 = 0

 

(x + 55)(x - 10) = 0

 

x = -55 or x = 10.  Since x can't be negative, x = 10 feet.