SOLUTION: Juan invested $24,000 into two stocks. The first stock paid a 4% dividend and the second stock paid a 3% dividend. If he received $800 in dividends in the first year, how much did

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Juan invested $24,000 into two stocks. The first stock paid a 4% dividend and the second stock paid a 3% dividend. If he received $800 in dividends in the first year, how much did      Log On

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Question 1169113: Juan invested $24,000 into two stocks. The first stock paid a 4% dividend and the second stock
paid a 3% dividend. If he received $800 in dividends in the first year, how much did he invest in
each stock?
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


First, a setup using a typical formal algebraic method....

"x amount at 4%, plus $24000-x amount at 3%, equals $800":

x%28.04%29%2B%2824000-x%29%28.03%29+=+800

Solve using basic algebra; I leave that to you.

Next, a quick and easy informal way to solve any 2-part mixture problem like this, if a formal algebraic solution is not required.

$24,000 all invested at 3% would yield $720 dividend

$24,000 all invested at 4% would yield $960 dividend

The actual dividend, $800, is 1/3 of the way from $720 to $960. (Picture the three numbers on a number line; from 720 to 960 is a difference of 240, from 720 to 800 is a difference of 80, 80/240 = 1/3.)

That means 1/3 of the total was invested at the higher rate.

ANSWER: 1/3 of $24,000, or $8000 was invested at 4%; the other $16,000 at 3%.

CHECK: .04(8000)+.03(16000) = 320+480 = 800