anne-sophie invested some of her 20k in bonds that made an 8% profit and the rest in bonds that made a 7% profit. If the profit on the 8% bonds was $700 more than the profit on the 7% bonds, how much did anne-sophie invest in the 7% bonds?

Answer 1

Let's denote the amount Anne-Sophie invested in the 8% bonds as \( x \) and the amount invested in the 7% bonds as \( 20000 - x \).

The profit from the 8% bonds can be expressed as: \[ 0.08x \]

The profit from the 7% bonds can be expressed as: \[ 0.07(20000 - x) \]

According to the problem, the profit from the 8% bonds was $700 more than the profit from the 7% bonds. We can write this as: \[ 0.08x = 0.07(20000 - x) + 700 \]

Now, let's simplify and solve for \( x \):

1. Distribute the 0.07 on the right side: \[ 0.08x = 1400 - 0.07x + 700 \] Combine the constants: \[ 0.08x = 2100 - 0.07x \]

2. Add \( 0.07x \) to both sides: \[ 0.08x + 0.07x = 2100 \] \[ 0.15x = 2100 \]

3. Divide both sides by 0.15: \[ x = \frac{2100}{0.15} = 14000 \]

Now that we have found \( x \), which is the amount invested in the 8% bonds, we can find the amount invested in the 7% bonds: \[ 20000 - x = 20000 - 14000 = 6000 \]

Thus, Anne-Sophie invested \(\boxed{6000}\) dollars in the 7% bonds.