SOLUTION: My son has 2 problems.
(1) A boy is mowing a field 40 rods and 20 rods rectangular. How wide a border must he cut in order that 3/4 of the mowing will have been completed?
(2)
Question 274883: My son has 2 problems.
(1) A boy is mowing a field 40 rods and 20 rods rectangular. How wide a border must he cut in order that 3/4 of the mowing will have been completed?
(2) Solve for x and y. 3X + 8y=-5 and x^2- 2XY=12.
Thank you. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! (1) A boy is mowing a field 40 rods and 20 rods rectangular.
How wide a border must he cut in order that 3/4 of the mowing will have been completed?
:
Find the area of the field, 40 * 20 = 800 sq/rds
Mowed area has to equal .75(800) = 600 sq/rds
That leaves 200 sq/rds unmowed
:
let x = the width of the swath around the unmowed area
unmowed length * unmowed width = 200 sq/rd
(40-2x)*(20-2x) = 200
FOIL
800 - 80x - 40x + 4x^2 = 200
Arrange as a quadratic equation
4x^2 - 120x + 800 - 200 = 0
:
4x^2 - 120x + 600 = 0
Simplify, divide by 4
x^2 - 30x + 150 = 0
Use the quadratic formula to solve for x, (only one solution will make sense)
a=1, b=-30, c=150
I got x ~ 6.34 rods is the width to mowed
;
:
(2) Solve for x and y.
3X + 8y =-5 and x^2- 2XY = 12.
:
try to get the 2nd equation in a form where we can eliminate y
x^2 - 2xy = 12
x(x - 2y) = 12
x - 2y =
Multiply by 4 and add the 1st equation
:
3x + 8y = -5
4x - 8y =
---------------------- eliminates y, find x
7x + 0y = -5 +
7x + 5 - = 0
multiply by x
7x^2 + 5x - 48 = 0; hopefully an equation we can factor
(7x-16)(x+3) = 0
Two solutions
7x = 16
and
x = -3
Use the integer solution in the 1st equation to find y
3x + 8y = -5
3(-3) + 8y = -5
-9 + 8y = -5
8y = -5 + 9
8y = +4
y =
y = +.5
:
Our solution: x=-3; y=+.5
:
:
See if that works in the 2nd equation
x^2- 2XY = 12.
-3^2 - 2*-3*.5 = 12
9 - (-3) = 12
9 + 3 = 12; so it works, the value x = 16/7 may work too, but you can check that out yourself
