I need Algebra 1 help. Can you help me?

Question

I understood the first problem, but this one is stumping me. Here's the math problem:
In the period of a year, an investor lost twice as much as he gained. If he originally had $10,000 and now has $8000, what amount did he gain and what did he lose?

Answer 1

Answer: Gain (G) = $2,000; Loss (L) = $4,000

Algebra word problems are solved by translating the words into equations. This is called setting up the problem (or equations). There are different ways to set up equations, depending on how you approach the problem (how you orgranize the words). You have two unknowns, "gain" and "loss". A basic theorem of algebra (actually, linear algebra, which is the common algebra taught in middle or high school) is that a problem with two unknowns requires two independent equations. After setting up the equations, you use substitution to solve for the unknowns. So here is one way to set up your problem and solve for the solutions (gain and loss).

First note that gains and loss are the total gains and losses (not net gain or loss). So an investment starts at ten thousand dollars, then has a total gain, called G, minus a total loss, called L, both being totals over the year, and this results in a final investment of eight thousand dollars. The first equation states the above and is:

10,000 + G - L = 8,000 (Equation 1)

(Note that in this equation L is a positve number. The equation could have been set up to take loss L as a negative number. You just have to be consistent.)

The next bit of information is that the Loss (L) is twice the Gain (G) (taking both as positive numbers. This is expressed mathematically as:

Loss L = 2G (2 times Gain, G) (Equation 2)

Substituting Eq. 2 into Eq 1 gives the following:

10,000 +G-2G = 8,000 (Equation 3)

Eqn. 3 can be rearranged to give
10,000 - 8,000 = 2G - G

Now simplify (add/subtract) to give
2,000 = G
and rearrange in the standard position (unknown on the left)
G = 2,000

Next use Equation 2 and the answer for Gain (G), to solve for Loss (L):

L = 2G (Equation 2 copied here)

Which gives, from solution for G=2,000:
L = 4,000

Next check: 10,000 + 2,000 - 4,000 = 8,000
So answers G=2,000 and L=4,000 are correct.

Note: This problem could be solved by "thinking it through", not using formal algebra methods, but more complicated problems require algebra and other math tools.

Answer 2

Gotta learn the lingo, miss nerd rules.
Let x be the amount gained.
Let 10,000 + x be his amount after his gain
Let 10,000 + x -2x be the amount he has now.
Since this is 8000, 8000 = 10000-x, and x =2000.

Answer 3

Suppose the investor gained x and lost 2x
Then
10000+x-2x=8000
which means x=2000
So he gained 2000 and lost 4000

Answer 4

Let x be his gain.
Makes sense that he lost 2x, right?
So, Start + gain - Loss = What's left
10000 + x -2x =8000
x-2x = 8000-10000
-x = -2000
x=2000

So 2x =4000
He gained 2000, lost 4000

Check: 10000+2000-4000 = 8000

It sounds to me like you've gained access to my stock market dealings!

Answer 5

Let x= amount gained, 2x= amount lost

10000-2x+x=8000
-1x=-2000
x=2000
2x=4000

10000-4000+2000=8000
6000+2000=8000
8000=8000

Answer 6

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Answer 7

Let X = amount of gain
Amount of loss = 2X
10,000 + X - 2X = 8,000 - Plug values into the equation
10,000 - X = 8,000 - Combine X terms.
2,000 - X = 0 - Subtract 8,000 from each side
2,000 = X - Add X to each side
$10,000 + $2,000 - $4,000 = $8,000 - A true statement.

Answer 8

10000-2x+x=8000
2000=x
gained 2000
lost 4000