Melanie receives an annual income of $684 from investing in stocks that earn 6% interest and bonds that earn 8% interest. If the investments were interchanged, her income would decrease by $24. Find the amount she invested in bonds originally.

The original amount invested in bond is $5,400.

Step-by-step explanation:

Given:

Interest on stocks = 6%, or 0.06

Interest on stocks = 8%, or 0.08

Let A represents the original amount invested in stocks and B represents the original amount invested in bonds. We can therefore have original income as follows:

0.06A + 0.08B = $684 (1)

Sine Malenie's income would decrease by $24 if the investments were interchanged, this implies that we will have:

0.08A + 0.06B = $684 - $24

0.08A + 0.06B = $660 (2)

From equation (2), we can solve for A as follows:

0.08A = $660 - 0.06B

Divide through by 0.08, we have:

A = $660/0.08 – (0.06/0.08)B

A = $8,250 – 0.75B

Substituting A = $8,250 – 0.75B into equation (1) and solve for B, we have:

0.06($8,250 – 0.75B) + 0.08B = $684

$495 – 0.045B + 0.08B = $684

Rearranging, we have:

– 0.045B + 0.08B = $684 - $495

0.035B = $189

B = $189 / 0.034

B = $5,400

Therefore, the original amount invested in bond is $5,400.