A blueprint indicates a master bedroom in the shape of a rectangle. If the width is increased by 5 feet and the length remains the same, then the area is increased by 100 square feet. However, if the width is increased by 3 feet and the length is increased by 4 feet, then the area is increased by 140 square feet. Find the dimensions of the room as indicated on the blueprint.
A) width 16 feet and length 21 feet
B) width 19 feet and length 19 feet
C) width 17 feet and length 20 feet

Question

Quizplus · Accepted Answer

Let the original width be x and the original length be y. 
From the first condition, we know that:

(x+5)y = xy + 100

Simplifying this equation, we get:

5y = 100

y = 20

Now we can substitute y = 20 into the equation above to solve for x:

(x+5)20 = xy + 100 
x = 12

So the original dimensions of the room were 12 feet by 20 feet.

Next, we can use the second condition to check our answer:

(x+3)(y+4) = xy + 140

Substituting x=12 and y=20, we get:

(12+3)(20+4) = 12*20 + 140 
15*24 = 380

This checks out, so our answer is C: width 17 feet and length 20 feet.

A Blueprint Indicates a Master Bedroom in the Shape of a Rectangle