Fairly easy math question for somebody who is good at word problems.?

Question

The width of a rectangle is 4 m less than one third of the length. If the perimeter of the rectangle is 56 m, find the dimensions of the rectangle.

1 m = 100 cm

Answer 1

Start by forming some equations from the problem. The first sentence shows us W=L/3-4. Since the perimeter is 56 meters, we also know 2L+2W=56. With these two equations, we can solve for the variables!

Substitute L/3-4 in for W in the second equation:
2L+2(L/3-4)=56 Then simplify:
2L+2L/3-8=56 (factor through)
2L+2L/3=64 (add 8 to both sides)
8L/3=64 (add L terms)
8L=192 (multiply both sides by 3)
L=24 (divide both sides by 8)

Then put L into one of our original equations to solve for W:
W=L/3-4
W=24/3-4
W=4

So one side has a length of 4 meters, the other a length of 24 meters.

Answer 2

24m by 4m.

Call the length L. Then the width is 1/3 L - 4. Perimeter is twice the length plus twice the width so P = 56 = 2L + 2 * (1/3 L - 4) = 2L + 2/3 L - 8. Rearranging, one gets: 8/3 L = 64 and: L = 64 * 3/8 = 24.

So the length equals 24. One could then say 1/3 that is 8 and 4 shorter than 8 is 4, giving one 24m by 4m.

(One could also realize the length plus width equals half the perimeter or: 56/2 = 24 + width and so width = 4.)

Answer 3

Let L be the length

From the description of the width you can write the following equation:
W = (1/3)L - 4

Perimeter is 2(L + W). Substitute in for W:
56 = 2(L + (1/3)L - 4)
56 = 2L + (2/3)L - 8
56 = (8/3)L - 8
64 = (8/3)L
64(3/8) = L
8 * 3 = L
24 = L
L = 24

Now figure the width:
W = (1/3)L - 4
W = (1/3)24 - 4
W = 8 - 4
W = 4

The rectangle is 4 meters wide and 24 meters long.

Answer 4

OK

P = 2L + 2w
w = 1/3L - 4

56 = 2L + 2(1/3L -4)
56 = 2L + 2/3L - 8
64 = 2 2/3 L
64 = 8/3 L
24 = L

So the length is 24m. The w =
w = 1/3(24) - 4
w = 8-4
w = 4

Check

56 = 2(24) + 2(4) ??
56 = 48 + 8
56 = 56 YES!!

Hope that helps.

Answer 5

2*width+2*length = 56
2*4 + 2*length = 56

2*length = 56-8

length = 48/2
length = 24

Answer 6

1) Say that: x = Steve 2x + 3 = Ken x - 5 = Len Add them all together and set that equal to 50: x + 2x + 3 + x - 5 = 50 Then you get: 4x - 2 = 50 Add 2 to each side, then: 4x = 52 Then divide each side by 4, and you get: x = 13 Then you can find your answers from there, and you get: Steve had 13 coins, Ken has 29 coins, and Len has 8 coins. 2) Gary = x So: 5x = x + 16 Subtract x from each side: 4x = 16 Divide each side by 4, and get: x = 4 So: Gary has 4 coins, and Geri has 20 coins. 3) x = Ty 2x - 2 = x + 23 Add 2 to each side: 2x = x + 25 Subtrach x from each side, then: x = 25 So: Ty has 25 coins, and Kai has 48 coins. 4) Let: x = Lary 2x - 3 = Barry and 3x + 20 = Sherry. Add all three of those together and set it equal to 65: x + 2x - 3 + 3x + 20 = 65 Then you get: 6x + 17 = 65 Subtract 17 from each side, and get: 6x = 48 Divide each side by 6, then you get: x = 8 So: Larry has 8 coins, Barry has 13 coins, and Sherry has 44 coins. I HOPE THIS HELPED!

Answer 7

perimeter=2(l+b)
56=2(1/3x-4+x)
56=2(x-12+3x/3)
56=2(4x-12)/3
56/2=4x-12/3
28=4x-12/3
84=4x-12
84+12=4x
96=4x
24=x
so the length is 24m and 1/3*x= width, the width is 4m

Answer 8

lets the width be w, and the length be y

so, w=(1/3)y-4 -------->1st equation
2w+2y=56 ---------->2nd equation
so, w+y=28
w=28-y
then do substitution,
(1/3)y-4=28-y
(4/3)y=32
y=24

so,w=28-24=4

so the width is 4m and the length is 24m

Answer 9

P=2L + 2W
W= 1/3 L - 4m
L=?
P=56m

solution:

56m = 2L + 2[1/3L -4]
56m = 2L + 2/3L - 8
8/3L = 56m + 8m
8/3L = 64m
8L = [64m]3
8L = 192m
L = 192m/8
L = 24m

W = 1/3L - 4m
W = 1/3[24] - 4m
W = 8m - 4m
W = 4m

TO CHECK:
P = 2L + 2W
56m = 2[24m] + 2[4m]
56m = 48m + 8m
56m = 56m

Answer 10

Indeed not a very difficult problem as is seen from all the answers which are correct.