SOLUTION: the park's width is 70m more than half the length with the total perimeter of 1280m what is the width and length of the park's perimeter

Question 174982: the park's width is 70m more than half the length with the total perimeter of 1280m what is the width and length of the park's perimeter
Found 3 solutions by checkley75, ankor@dixie-net.com, actuary:
Answer by checkley75(3666)   (Show Source): You can put this solution on YOUR website!
W=L/2+70
2L+2W=1,280
2L+2(L/2+70)=1,280
2L+2L/2+140=1,280
2L+L=1,280-140
3L=1,140
L=1,140/3
L=380 IS THE LENGTH.
W=380/2+70
W=190+70
W=260 IS THE WIDTH.
PROOF:
2*380+2*260=1,280
760+520=1,280
1,280=1,280

Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
the park's width is 70m more than half the length
W = .5L + 70
:
the total perimeter of 1280m
2L + 2W = 1280
:
Simplify, divide by 2
L + W = 640
Substitute (.5L+70) for W in the above equation
L + (.5L + 70) = 640
:
1.5L = 640 - 70
:
1.5L = 570
L =
L = 380 meters is the length
:
Find the width
W = .5(380 + 70)
W = 190 + 70
W = 260 m is the width
:
:
Check solution in the perimeter equation
2(380) + 2(260) =
760 + 520 = 1280m confirms our solution

Answer by actuary(112)   (Show Source): You can put this solution on YOUR website!
The width of the park is w and thelength is l.
The equations that describe the situation are:
2l+2w=1280m (Equation #1)
w = (1/2)*l+70 (Equation #2)
Equation #1 can be rewritten as l = 640 - w
Substitute the value for l into equation #2
w = 1/2(640-w)+70 = 320 -(1/2)*w + 70
Putting the unknowns on one side of the quation.
w+(1/2)w=390
3/2w = 390
Solve for w
w = 390*(2/3) = 260 m
Substituting the value for w into equation #1, we have
2*l+2*(260m)=1280m
2*l = 1280m-520m = 760m
Solve for l
l = 380m

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