WORD PROBLEM: Solve the word problem.

Question

Steven needs to purchase enough wallpaper to cover a wall measuring 84 square feet. If the width is 5 feet more than the length, what are the dimensions of the wall?

   

Length: 

  

Width: 

Answer 1

The question is asking for the value of two variables. Luckily, they gave you two equations with which to determine them.

First, they give you the area: L * W = 84.

Second, they give you a relation of one to the other. Width (W) is (=) 5 more than (+) the length (L): W = 5 + L.

Since this is already well set up for substitution, we'll go that route.

L * W = 84

L * (5+L) = 84

Then we distribute.

5L + L² = 84

Since this is now a quadratic equation, we should set one side equal to zero by subtracting 84 from both sides.

L² + 5L - 84 = 0

At this point, you can use the quadratic equation or you can factor.

(L - 7)*(L + 12) = 0

Now we set each side part to zero separately.

L - 7 = 0 L + 12 = 0

L = 7 L = -12

Since the length can't be negative, then it must be 7. Since width is 5 more than length, width must be 12.