Answer: x=4,-4 Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula
(a) x = 4
First, let's calculate the area of the path as a function of x. You have two paths, one of them is 8 ft long by x ft wide, the other is 16 ft long by x ft wide. Let's express that as an equation to start with.
A = 8x + 16x
A = 24x
But the two paths overlap, so the actual area covered will smaller. The area of overlap is a square that's x ft by x ft. And the above equation counts that area twice. So let's modify the equation by subtracting x^2. So:
A = 24x - x^2
Now since we want to cover 80 square feet, let's set A to 80. 80 = 24x - x^2
Finally, let's make this into a regular quadratic equation and find the roots.
80 = 24x - x^2
0 = 24x - x^2 - 80
-x^2 + 24x - 80 = 0
Using the quadratic formula, you can easily determine the roots to be x = 4, or x = 20.
Of those two possible solutions, only the x=4 value is reasonable for the desired objective.
(b) There were 2 possible roots, being 4 and 20. Both of those values, when substituted into the formula 24x - x^2, return a value of 80. But the idea of a path being 20 feet wide is rather silly given the constraints of the plot of land being only 8 ft by 16 ft. So the width of the path has to be less than 8 ft (the length of the smallest dimension of the plot of land). Therefore the value of 4 is the most appropriate.
Since your trying to round 103.459 to the nearest whole number, you have to find if the tens place is a 5 or greater. If not, the whole number stays the same. In the instance, 103.459 can't be rounded up more, because 4 is not able to round it to 104. So your answer would be 103.
ANSWER
x=3, y=-4
EXPLANATION
The given system is :
First equation:
Second equation:
Let us multiply the first equation by 7 to get,
Third equation;
Let us multiply the second equation too by 10 to get,
Fourth equation:
Subtract the fourth equation from the third equation:
Divide both sides by 59.
Put y=-4 into the second equation and solve for x.
The solution is x=3, y=-4
