A wood beam 48 inches in length is cut into two smaller beams. If one

Using one variable (as the posters above have done) is preferable to 2 variables.
But, just for kicks, let's solve it with 2 variables.

Let S = length of SHORTER beam
Let L = length of LONGER beam

A wood beam 48 inches in length is cut into two smaller beams.
So, we can write: L + S = 48

One of the new beams is 20 inches longer than the other
We can write: L = S + 20
Subtract S from both sides to get: L - S = 20

We now have the following system:
L - S = 20
L + S = 48

ADD the two equations to get: 2L = 68
Divide both sides by 2 to get: L = 34

Answer: E

Cheers,
Brent

We can also solve this by testing the answer choices

let's start with answer choice C

C) 28
This means the longer beam has length 28
Since the longer bean is 20 inches longer than the shorter beam, this means the shorter beam has length 8
If we add the two lengths we get: 28 + 8 = 36, but we're told the combined length must be 48
ELIMINATE C

NOTE: Using answer choice C (28), the combined length (of 36 inches) was not long enough. This means we need the longer beam to be LONGER than 28 inches.
So, we can ELIMINATE A and B as well

Now try D
D) 30
This means the longer beam has length 30
Since the longer bean is 20 inches longer than the shorter beam, this means the shorter beam has length 10
If we add the two lengths we get: 30 + 10 = 40, but we're told the combined length must be 48
ELIMINATE D

At this point, since we have already eliminated A, B, C and D, answer choice E MUST be correct.
That is, we need not test it, since doing so would waste valuable time.

That said, let's test it (for fun!!!)
E) 34
This means the longer beam has length 34
Since the longer bean is 20 inches longer than the shorter beam, this means the shorter beam has length 14
If we add the two lengths we get: 34 + 14 = 48
PERFECT!!