Question

A rectangular lot whose perimeter is 280 ft is fenced along 3 sides. An expensive fence along the lots length cost $35 per foot. An inexpensive fencing along the 2 side widths costs only $5 per foot. the total coast of the 3 sides is 3275. what are the dimensions? @jim_thompson5910

Answer 1

let x = length, y = width

we have this picture

Answer 2

okok

Answer 3

the perimeter is 280, so all 3 sides add to 280

y+x+y = 280

x+2y = 280

x = 280 - 2y

Answer 4

the expensive fence (that runs along the length x) is $35 a ft and the inexpensive fencing (that runs along the width y) is $5 a foot

so the total cost is

35x + 5y + 5y = 35x + 10y

Answer 5

we are told the total cost is $3275, so

35x + 10y = 3275

35(280-2y) + 10y = 3275 ... plug in x = 280 - 2y

now solve for y

Answer 6

okay hang on

Answer 7

ok

Answer 8

y= 108.75?

Answer 9

good

Answer 10

use that to find x

Answer 11

it does? woah. you are a better explainer than my teacher!

Answer 12

I'm glad it's all clicking now

Answer 13

what do you get for x?

Answer 14

x=62.5?

Answer 15

perfect on both

Answer 16

gracias for your help

Answer 17

oh wait...the perimeter of the lot is 280

not the total fencing is 280

so I messed up, I'm sorry, let me fix it

Answer 18

oh okay is fine

Answer 19

the perimeter of the lot is 280,

so we have 4 sides (two of them x, two of them y) that add to 280


x+y+x+y = 280

2x+2y = 280

2(x+y) = 280

x+y = 280/2

x+y = 140

y = 140 - x

------------------------------

Then we plug this into the second equation (that is still the same) and solve for x

35x + 10y = 3275

35x + 10(140-x) = 3275

35x + 1400-10x = 3275

25x + 1400 = 3275

25x = 3275 - 1400

25x = 1875

x = 1875/25

x = 75

and use this to find y

y = 140 - x

y = 140 - 75

y = 65

So the length is 75 and the width is 65

Answer 20

I thought we only had 3 sides?

Answer 21

I originally thought that too, but they are talking about the perimeter of the lot, not the total fencing put up

Answer 22

ohhhhhhhhhhhhh

Answer 23

yeah definitely got me too

Answer 24

its a rectangle!

Answer 25

yes it is, one side isn't fenced because it's probably against a wall already there

Answer 26

the longer dimension would be 75 right

Answer 27

correct

Answer 28

i only have one chance

Answer 29

thanks

Answer 30

you're welcome

Answer 31

perfect.it all makes sense.. Goodnight!

Answer 32

I'm glad it does, good night

Answer 33

waiiit. i have o admit I snuck an used mathway.com for a few problems could yo explain one really quick?

Answer 34

sure and I use calculators all the time

Answer 35

what do you need an explanation on?

Answer 36

4a+7b=-8
8a+4c=56
6b+4c=-8

Answer 37

there are a number of ways to do this, most ways lead to using fractions

let's see if this method has us using the least amount of fractions

Answer 38

solve the second equation 8a+4c=56 for c to get

8a+4c=56

4c=56 - 8a

c=56/4 - 8a/4

c = 14 - 2a

now plug this into the third equation

6b+4c=-8

6b+4(14 - 2a)=-8

6b + 56 - 8a = -8

-8a + 6b = -8 - 56

-8a + 6b = -64

with me so far?

Answer 39

yes

Answer 40

now we have the 2 equations

4a+7b=-8
-8a + 6b = -64

how do we solve this system?

Answer 41

lets multiply the top equation by 2

Answer 42

good choice that gives you

4a+7b=-8

2*(4a+7b)=2*(-8)

8a + 14b = -16

Answer 43

so

8a + 14b = -16
-8a + 6b = -64
---------------
0a + 20b = -80

20b = -80 ---> b = ???

Answer 44

oh and I added those equations

Answer 45

b=-4

Answer 46

good, then use this to find a,c

Answer 47

so go back to any equation with only a and b in them, plug in b = -4, then solve for 'a'

Answer 48

4a=13

Answer 49

nah thats not right

Answer 50

a,b,c are all whole numbers

so that looks off

Answer 51

4a+7(-4)=-8

Answer 52

8a + 14b = -16

8a + 14(-4) = -16

8a - 56 = -16

...
...
...

a = ???

Answer 53

wait.

Answer 54

oh we multiplied by 2 didnt we

Answer 55

yes we could use any equation with a,b in it

I just happened to pick that one

Answer 56

a=5

Answer 57

good

Answer 58

then use this to find c

Answer 59

6b+4c=-8

Answer 60

you could use that equation or you could use

c = 14 - 2a

Answer 61

this one is much easier since c is already isolated

Answer 62

c=14-10
c=4

Answer 63

so

a = 5, b = -4, c = 4

Answer 64

perfect. thank you. okay this time actually goodnight lol

Answer 65

sure thing, good night to you as well