Helen Weller invested $10,000 in an account that pays 10% simple interest. How much additional moneymust be invested in an account that pays 13% simple interest so that the average return on the two investments amounts to 11%?

I know the answer is $5,000.00 but I am unsure how to set up the problem to show that solution. Could you help me?

Ok, let's first give the amount a name, say 'x'

(13% of x) + (10% of 10000) gives (11% of x + 10000) where x+10000 is the total sum.

So, in numbers;

\frac{13x}{100} +\frac{10(10000)}{100} = \frac{11(x+10000)}{100}

When you simply, solve for x and you're done. Post back if you have any difficulties.

Hope it helped! :)

$10,000 invested in an account that pays 10% simple interest.
How much additional money must be invested in an account that pays 13% simple interest so that the average return on the two investments amounts to 11%?

I know the answer is $5,000.00

$10000 x 0.10 = $1000 is the annual interest at 10% on $10,000

Let A be the amount that's invested at 13%

The amount earning interest at 10% plus the amount that's invested at 13% equals the two amounts as if they had been invested at 11%. This is the equation that results.

($10000 x 0.10) + (A x 0.13) = ($10000 + A) x 0.11

We need to solve for A and check that it's correct by substituting back into the equation.

I see that Unknown008 beat me to the punch.