rosalinda invested some of her 15k in bonds that made a 6% profit and the rest in bonds that made a 10% profit. If the profit on the 10% bonds was 1k, much more than the profit on the 6% bonds, how much did rosalinda invest in the 6% bonds?

1 answer

Let \( x \) be the amount Rosalinda invested in the 6% bonds. Therefore, the amount she invested in the 10% bonds would be \( 15000 - x \).

According to the problem, the profit on the 10% bonds was $1,000 more than the profit on the 6% bonds.

The profit from the 6% bonds can be expressed as: \[ 0.06x \]

The profit from the 10% bonds can be expressed as: \[ 0.10(15000 - x) \]

According to the information given: \[ 0.10(15000 - x) = 0.06x + 1000 \]

Now, let's solve this equation step by step:

  1. Expand the left side: \[ 1500 - 0.10x = 0.06x + 1000 \]

  2. Rearranging this gives: \[ 1500 - 1000 = 0.06x + 0.10x \] \[ 500 = 0.16x \]

  3. Now, solve for \( x \): \[ x = \frac{500}{0.16} = 3125 \]

Therefore, Rosalinda invested \( \boxed{3125} \) dollars in the 6% bonds.

To verify:

  • Amount invested in 10% bonds = \( 15000 - 3125 = 11875 \)
  • Profit from 6% bonds = \( 0.06 \times 3125 = 187.5 \)
  • Profit from 10% bonds = \( 0.10 \times 11875 = 1187.5 \)

Now, check the condition: The profit on the 10% bonds is \( 1187.5 \), which is indeed \( 1000 \) more than the profit on the 6% bonds (\( 187.5 + 1000 = 1187.5 \)).

Thus, the solution is confirmed correct, and Rosalinda invested \( \boxed{3125} \) dollars in the 6% bonds.