Question

a sales representative invests in a stock paying 8% dividends. a research consultant invests $5,000 more than the sales representative in bonds paying 7% annual simple interest. the research consultants income from the investment is equal to the sales representatives. find the amount of the research consultants investment.

Explanation:

Step1: Let the sales - representative's investment be $x$.

The sales - representative's income from the 8% dividend - paying stock is $0.08x$. The research consultant's investment is $x + 5000$, and the income from the 7% bond is $0.07(x + 5000)$.

Step2: Set up the equation based on equal incomes.

Since the incomes are equal, we have the equation $0.08x=0.07(x + 5000)$.

Step3: Expand the right - hand side of the equation.

Using the distributive property, $0.08x=0.07x+0.07\times5000$, so $0.08x = 0.07x+350$.

Step4: Solve for $x$.

Subtract $0.07x$ from both sides: $0.08x−0.07x=350$, which gives $0.01x = 350$. Then $x=\frac{350}{0.01}=35000$.

Step5: Find the research consultant's investment.

The research consultant's investment is $x + 5000$. Substitute $x = 35000$ into it, we get $35000+5000=40000$.

Answer:

40000