One more word problem?

Question

First i would like to thank all that are helping me with this. I am not very bright when it comes to math.

Helen Weller invested $10,000 in an account that pays 12% simple interest. How much additional money must be invested in an account that pays 15% simple interest so that the total interest is equal to the interest on the two investmentsat the rate of 13%.

Answer 1

Let n be the amount in the 2nd account:

The interest on the first acount will be:
10000 x 12%

The interest on the second account will be:
n x 15%

All together you will have (10000 + n) dollars at 13%
(10000 + n) x 13%

The first two expressions should add to be the third:
10000 x 12% + n x 15% = (10000 + n) x 13%

If you like, you can ignore the percent signs( equivalent to multiplying both sides by 100):

12 x 10000 + 15 x n = 13 x (10000 + n)

120000 + 15n = 130000 + 13n

Subtract 13n from both sides:
120000 + 2n = 130000

Subtract 120000 from both sides:
2n = 130000 - 120000
2n = 10000

Divide both sides by 2:
n = 5000

So you need to invest $5000 in the other account.

As a double-check:
The first account will earn $10,000 x 12% = $1,200
The second account will earn $5,000 x 15% = $750

This is equivalent to $15,000 earning 13% = $1,950

Answer:
You must invest $5,000 in the second account.

Answer 2

10000*0.12 = 1200
X=investment required
Y= the interest of this investment

X * 0.15 = Y
(X+10000)*0.13 = Y + 1200

0.13X + 1300 = 0.15X +1200
0.02X = 100
X = 5000
$5000 must be invested in the 15% account.

Answer 3

additional money required
= (13 -- 12)/(15 -- 13) of $10000
= $5000

Answer 4

10000*0.12+x*0.15=(10000+x)*0.13
1200+0.15x=1300+0.13x
0.02x=100
x=$5,000