Question

What equations would I use to set this up?

A picture frame has a perimeter of 40 inches. Its length is 2 inches greater than one-half its width. Let w represent the width of the picture frame, and let l represent the length.

Answer 1

the first step is to give "names" to the unknowns.

They already did this:
Let w represent the width
and L is the length

Answer 2

the second step is to remember or look in your notes or google , and find the definition (and formula) for the perimeter of a rectangle.
Can you do that ?

Answer 3

(I left out the step where you figure out that a picture frame is in the shape of a rectangle)

Answer 4

I know the rectangle formula. I need two equations though. I'm trying to figure out where the second one comes from.

Answer 5

first write down the formula for the perimeter

Answer 6

That's just 2(l+w)

Answer 7

ok, but use the info from the first sentence:
picture frame has a perimeter of 40 inches.

to write an equation

Answer 8

Oh! Okay. I see what you mean now.

Answer 9

and what equation do you get ?

Answer 10

picture frame has a perimeter of 40 inches.

means the perimeter is 40 inches
but the perimeter is also 2(L+w)

we can say if the perimeter is 40 inches and the perimeter is 2(L+w)
then it must be that
2(L+w)= 40

btw, I am using L instead of l, because lower case L looks too much like a 1 (one)

Answer 11

40=2((L+2)+(1/2w))
Did I do that right?

Answer 12

Wow, I did not do that right.

Answer 13

I would do things in small steps.

and each step should make sense.

hopefully, if you think about it,
2(L+w) = 40
makes sense.

in words, that says the perimeter ( i.e. 2(L+w) ) equals (is) 40

Answer 14

one way to thing about it is give the perimeter a name, like P
we would write the formula
P= 2(L+w)

then we would use the info
picture frame has a perimeter of 40 inches.
to write
P= 40

now if 40 = P, and at the same time 2(L+w) = P
then 40= 2(L+w)

does the logic make sense?

Answer 15

Yes. It does make sense.

Answer 16

now on to the next sentence.
Its length is 2 inches greater than one-half its width.

Answer 17

We need to "translate" that into "math"

Let's go in steps:
Its length is

the "name" we are using for the length is L
L is

but "is" almost always translates to =

L =

Answer 18

Its length is 2 inches greater than one-half its width. becomes

L = 2 inches greater than one-half its width

Answer 19

can you try translating
one-half its width

?

first, replace width with its name

Answer 20

I just figured out what I was doing. Thank you for your help so far! I appreciate it. (:

Answer 21

can you try translating
one-half its width

?