How do I solve for L in this formula?

Question

I have this formula:
P=L*.10W+.5L+.5W

I have to solve it for L, meaning that I have to reconfigure the formula so that L is on one side. For the life of me, I cannot figure this out.

(It's not important, but P is price, L is length, and W is width.)

Answer 1

First, let's multiply through by 10 to clear the decimals:

10P = L*1W + 5L + 5W

Next, get all the L terms on one side subtracting 5W:

10P - 5W = 1LW + 5L

Now you can factor out an L on the right side (reverse the distributive property:

10P - 5W = L(W+5)

Finally, divide by (W+5):

(10P - 5W)/(W+5) = L

Answer 2

You can keep your life! There is an answer!
P = L*.10W + .5L + .5W

When you have an expression that has nothing to do with the term you are solving for, you move it to the other side. If it was being added, you subtract it. If it was being subtracted you add it. If it was being multiplied, you divide it. If it was being divided you multiply it. In other words, whatever operation is going on you do the opposite.
First let's move ".5W" because it has nothing to do with "L". Since ".5W" is being added on the right we can move it to the left side by subtracting by ".5W" on both sides, so
P - .5W = L*.10W + .5L
Now we can factor out "L" on the right side because it is common
P - .5W = L(.10W + .5)
Before each term was being multiplied by "L", but we brought it on the outside. You can check by multiplying through by "L" again and you'll get the same thing as the line before. Now since what we are looking on the right hand side is L being multiplied by ".10W + .5", which has nothing to do with "L", we move it by dividing. So now we have
(P - .5W) / (.10W + .5) = L

Answer 3

jenh's answer is nice, althought the decimal clearing is indeed unnecessary.

I think the following guidelines will help you for ALL of your problems of this caliber, and not just this one.

1) To make life easy, clear out any fractions by multiplying everything by the LCD.

2) Distribute to bust open any parentheses. This frees up all your terms to move around as you please.

3) Segregate all terms containing the desired variable (in this case, L) on one side ot the equal sign, and all other terms on the other side, by adding and subtracting as necessary.

4) Factor out the desired variable from whichever side it is on (this is made possible by the segregation move: since everything has that variable, it must be a common factor. By getting ALL of that variable on one side, you are guranteed to be left with just one of that variable after factoring it out).

5) Finally, divide both sides by whatever parentheses is following the factored-out variable.

Answer 4

P = L*10W +5L + 5W
P = 10LW + 5L + 5W
P - 5W = 10LW + 5L
P - 5W = 5L(2W+1)
(P-5W) / (2W+1) = 5L
L = (P-5W) / (2W+1) * 1/5

Cheers

Answer 5

subtract .5w from each side, subtract .5L from each side, then divide .10W from each side.

so it would be
P-.5L-.5W/.10W

you cannot reduce the w's because you are subtracting up top..

hope i helped!