Question

CRAFTS Madelyn cut a 60-inch pipe cleaner into two unequal pieces, and then she used each piece to make a square. The sum of the areas of the squares was 117 square inches. Let x= the length of one piece. Write and solve an equation to represent the situation and find the lengths of the two original pieces.

Answer 1

http://openstudy.com/users/directrix#/updates/513ffb2be4b0f08cbdc8b4ce

Answer 2

Here is where we left off. Read the info at the link first.

(x/4)² + [(60 -x)/4]² = 117

Solve for x.

Answer 3

does that equal 2x^2 -120x+243=0 ?
and from there solve for x with quadratic formula ?

Answer 4

I think I have:

x^2 - 60x +1800 = 0

Let's check our products.

Answer 5

Mine is wrong.

Answer 6

I think your product is also incorrect.

Answer 7

Let us multiply again.

Answer 8

i got x^2/16 + x^2-120x+360/16 = 117

Answer 9

(x/4)² + [(60 -x)/4]² = 117


x^2/16 + (x^2 -120x + 360) /16 = 117

Answer 10

Let's multiply this one more time:

[(60 -x)/4]² = [(60 -x)/4] * [(60 -x)/4] = (60 - x)^2 / 16

Answer 11

(60 - x)^2 / 16 =

This part is:
(60 - x)^2
= 3600 - 120x + x^2

Answer 12

x^2/16 + (x^2 -120x + 3600) /16 = 117

Multiply through by 16

Answer 13

Eventually, it factors into (x - 24)*(x-36) = 0

Answer 14

isn't 16 a common denominator because it's adding fractions?

Answer 15

Yes, it is.

Answer 16

it factors into (x - 24)*(x-36) = 0
so x = 24 or x = 36.

Which ones of those makes sense in the context of the problem?

Answer 17

I don't get how you got to that stage ..
from x^2/16 + (x^2 -120x + 3600) /16 = 117
doesn't it reduce to
x^2+ X^-120x+3600 = 117
so you subtract 117 to 3600?

Answer 18

Did we agree up to this point?

x^2/16 + (x^2 -120x + 3600) /16 = 117

Answer 19

yeess

Answer 20

So far, so good up until that point.

Answer 21

or is it x^2-120x+36-/16 = 117
so you multiply 16 with 117
to get 2x^2-120x-1512=0 ?

Answer 22

Check the constant term. It is not correct.

Answer 23

from that i got x=42
im so confuseeed

Answer 24

\[\frac{ x^2}{16} + \frac{(x^2 -120x + 3600)}{16} = 117\]\[\frac{ x^2+(x^2 -120x + 3600)}{16} = 117\]Multiply both sides by 16
\[16\times \frac{ x^2+(x^2 -120x + 3600)}{16} = 16\times 117\]

Answer 25

oooh i understand
9x-34) (x-36)
thank you (: my calc. was wrong

Answer 26

x^2/16 + (x^2 -120x + 3600) /16 = 117
-------------------------------
Multiply by 16.

x^2 + (x^2 -120x + 3600) = 16*117

2 x^2 - 120 x + 3600 = 1872 @jenna_kwak Did you get this.

I lost a denominator along the way and then multiplied incorrectly.

Answer 27

i got 2x^2-120x+3600=1872
subtracted and got
2x^2-120x+1728
factored
2(x^2-60x+864)
and got
(x-24) and (x-36)

Answer 28

2 x^2 - 120 x + 3600 = 1872
2 x^2 - 120 x + 1728 = 0

x^2 - 60 x + 864 = 0

(x-24)* (x-36) = 0
x = 24 and x = 36.

Such a good feeling when it finally all works out.

Answer 29

yes (:
the heart of math
thank you gus so much
im in precal and my algebra1 sister didnt get this
and i was struggling for like a hour -____-
thank you !

Answer 30

The struggle is how we get tough and good at solving these things. You never gave up. We'll give @Callisto a nod for catching that arithmetic error :).

Answer 31

I enjoyed the process. Now, explain it to your sister.

Answer 32

i am thank you (: