SOLUTION: A room is one yard longer than it is wide. At 75c per sq. yd. a covering for the floor costs S31.50. Find the dimensions of the floor.

Question 1069760: A room is one yard longer than it is wide. At 75c per sq. yd. a covering for
the floor costs S31.50. Find the dimensions of the floor.

Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
(W+1)*W*0.75 = 31.50
Are they asking you to solve using the quadratic formula or completing the squares? I'll complete the squares, the answer is the same either way you calculate it:
Rewrite:
3/4W(W+1) = 31.50 multiply both sides times 4/3:
W(W+1) = 42.00 Distributive Properties of multiplication:
W^2+W = 42
Now we have to complete the squares. This is a mechanical process, it's the same every time:
Take one-half of the coefficient of x and square it, then add it to both sides:
The coefficient of W is 1 (W = 1W, and 1 is the coefficient). Half of 1 is 1/2 and 1/2^2 = 1/2*1/2 = 1/4 Add 1/4 to both sides:
W^2+W+1/4 = 169/4
Factor the left side:
(W+1/2)^2 = 169/4 take the square root of both sides to get rid of the exponent
W+1/2 = 13/2
Because it's a quadratic equation, we get two possible answers:
:
W = 13/2-1/2 or W = -13/2-1/2
W = 6 or W = -7
We are not looking for a negative number, so throw away the -7 and try the 6:
:
(W+1)*W*0.75 = 31.50
(6+1)*6*0.75 = 31.50
7*6*0.75 = 31.50 Because of the properties of multiplication, you can multiply in any order you like. I'll go with 7*6 because I can do it in my head:
42*0.75 = 31.5 Multiply 42*0.75 and see what you get ;-)
:
Happy learning,
John

RELATED QUESTIONS
Quadratic Formula , A room is one yard longer than it is wide. At 75c per sq. yd. a... (answered by Fombitz)

Paul and Joan wish to buy floor covering that covers 150 square feet for their large... (answered by ikleyn,math_tutor2020)

A rectangle is twice as long as it is wide. If its area is 50 sq. yd., find the length. (answered by macston)

1.) Mary Anne Young has enough grass sees to cover 400 square feet. She wishes to grow... (answered by stanbon)

The rectangular floor of a new office building is 50 feet longer than it is wide. The... (answered by oberobic)

A rectangle is twice as long as it is wide. If its area is 50 sq. yd., find the length. (answered by JulietG,ewatrrr)

a dorm room at a college your sister is considering seems small. The room is rectangular... (answered by funmath)

What is the cost of carpeting a room that measures 15ft by 12 ft if the carpeting costs... (answered by Alan3354)

How do I find the dimensions the floor of a rectangular shed is 7feet longer than it is... (answered by Alan3354)