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
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