SOLUTION: 1. Find two consecutive integers such that the sum of there square is 85.
2. A garden area is 30ft long and 20ft wide. A path of uniform width is set around the edge. If the rem
Question 85444: 1. Find two consecutive integers such that the sum of there square is 85.
2. A garden area is 30ft long and 20ft wide. A path of uniform width is set around the edge. If the remaining garden area id 400ft ^2, what is the width of the path? Found 2 solutions by scianci, venugopalramana:Answer by scianci(186) (Show Source):
You can put this solution on YOUR website! 1. x = first integer
x + 1 = next consecutive integer
+ = 85 + + 2x + 1 = 85 + 2x + 1 = 85 + 2x - 84 = 0 + x - 42 = 0
(x + 7)(x - 6) = 0
x + 7 = 0 ; x - 6 = 0
x = -7 ; x = 6
x = -7 , x + 1 = -6 is one pair of solutions
x = 6 , x + 1 = 7 is another pair of solutions
2. Let x = width of the path
Garden area = 20(30) = 600
Remaining Garden area = (30 - 2x)(20 - 2x) = 400
600 - 100x + = 400 - 100x + 600 = 400 - 100x + 200 = 0 - 25x + 50 = 0 = = = = , =
23.31 , 1.69
23.31 is not feasible since the whole width is only 20 ft, so the answer is 1.69 ft.
You can put this solution on YOUR website! 1. Find two consecutive integers such that the sum of there square is 85.
N^2+(N+1)^2=85
N^2+N^2+2N+1=85
2N^2+2N-84=0
N^2+N-42=0
N^2+7N-6N-42=0
N(N+7)-6(N+7)=0
(N-6)(N+7)=0
HENCE N=6 OR -7
THE 2 INTEGERS ARE 6&7
OR -7 AND -6
2. A garden area is 30ft long and 20ft wide. A path of uniform width is set around the edge. If the remaining garden area id 400ft ^2, what is the width of the path?
GARDEN AREA =400 SQ.FT.
IF THE WIDTH OF PATH IS X FEET , THEN
LENGTH OF GARDEN = 30-X-X=30-2X
WIDTH OF GARDEN =20-X-X=20-2X
AREA OF GARDEN =(30-2X)(20-2X)=400
600-60X-40X+4X^2=400
4X^2-100X+200=0
X^2-25X+50=0
=2.2 FT
(
