Comment This is an area problem. The key words are 120 square feet and 12 feet longer. And of course width is a key word when you are reading this.
Formula Area = L * W
Givens W = W L = W + 12
Substitute and Solve Area = L* W 120 = W*(W + 12) W^2 + 12W = 120 square feet w^2 + 12w - 120 = 0
This does not factor easily. I would have thought that a graph might help but not if the dimension has to be to the nearest 1/100 of a foot. The only thing we can do is use the quadratic formula.
a = 1 b = 12 c = - 120
w = [ -b +/- sqrt(b^2 - 4ac) ]/(2a) w = [-12 +/- sqrt(12^2 - 4*(1)(-120)] / 2*1 w = [-12 +/- sqrt(144 - (-480)]/2 w = [-12 +/- sqrt(624)] / 2 w = [- 12 +/- 24.979992] / 2 The minus root has no meaning whatever. w = (12.979992) / 2 w = 6.489995 I'll round all this when I get done
L = w + 12 L = 6.489995 + 12 L = 18.489995
check Area = L * W Area = 6.489995*18.489995 Area = 119.999935 The difference is a rounding error
Answer L = 18.489995 = 18.49 feet W = 6.489995 = 6.49 feet
Note: in the check if you round first to the answer, LW = 120.0001 when you find the area for the check. Kind of strange how that nearest 1/100th makes a difference.
To mix cleaner and water you need to divide the bucket's capacity into 4.It's easy in this case as gallon is divided into quarts (1 gallon = 4 quarts).We know that one part will be cleaner, it means that you will need to use 1 quart of the cleaner. hope thats right
