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?

Question

GPT-4o mini · 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.