Can someone help me with this problem?

Question

I don't know how to set-up the problem, nor the procedures for it. The problem is:

Mark invested $6000 at 6% per year. How much money should she invest at 8% per year so that the annual income from the two investments is 7%?

Answer 1

Let x = amount invested at 8%
Then the total amount invested is 6000 + x

Let P = principal, R= rate, I = interesr

P | R | I=PxR
6000 | .06 | 360
x | .08 | .08x
6000+x | .07 | .07(6000+x)

360 + .08x = .07(6000 + x)
360 + .08x = 420 + .07x
.08x - .07x = 420 - 360
.01x = 60
x = 6000.

Therefore, mark should invest $6000 at 8%

Answer 2

Mark would simply invest the same amount of $6000 @ 8% which would be a total investment of $12000...see, you multiply $6000 X .06 =$360.00. Then multiply the same amount $6000 X .08= $480.00. That adds up to $840.00 interest on $12,000.00. Now, just prove it by $12,000.00 X 7% .07 and you get the same amount of interest, which is $840.00.

I am so curious....maybe someone can explain: When I answered this question, my answer was the first in line, now I return to the site and I am at the end of the line. Is there some way that people have of holding their place, then figuring out the answer and returning and finishing it? I'm not complaining, I'm just curious...to me, the answer was simple, I don't know why people have made it so complicated, unless this is for an algebra class.

Answer 3

let the investment at 8% = x
frame the equation with the given relation

6000*(6/100) + x*(8/100) = (x + 6000)*(7/100)

36000 + 8x = 7x + 42000

x = 6000

Answer 4

let x be the amount of money he invests at 8%

.06(6,000) is the interests he gains at 6$
.08x is the interest he gains at 8%
.07(x + 6000) is the interest he gains at 7% from both investment

.06(6000) + .08x = .07(x + 6000)
360 + .08x = .07x + 420
.01x = 60
x = 6,000

$6,000 at 8%

hope this helps

Answer 5

income = 6000* .06 + x *.08
must equal (6000 + x) *.07 = 6000 * .07 + x * .07

subtracting => 6000 * (.06 - .07) + x * (.08 - .07) = 6000 * -.01 = x * .01 = 0

This .01x = .01 * 6000
x = 6000, too

PS how is Mark a she ?