Question

On two investments totaling $13,500, Nelson lost 5% on one and earned 7 % onIf the other. If his net annual receipts were $327, how much was each investment?AnswerHow to enter your answer (opens in new inwindow)KeypadKeyboard Shortcuts2 Pointsat -5 %$at 7 %

Answer 1

We are given the following information

There are two investments totaling $13,500.

Nelson lost 5% on one and earned 7% on the other.

The net annual receipts were $327.

Let x and y represent the amount of each investment.

Using the above information, we can set up the following two equations

`\begin{gathered} x+y=13,500\quad eq.1 \\ -0.05x+0.07y=327\quad eq.2 \end{gathered}`

Let us solve the above system of linear equations using the substitution method.

Re-write eq.1 in terms of x or y

`y=13,500-x\quad eq.1`

Now, substitute eq.1 into eq.2

`\begin{gathered} -0.05x+0.07y=327 \\ -0.05x+0.07(13,500-x)=327 \\ -0.05x+945-0.07=327 \\ -0.12x+945=327 \\ -0.12x=327-945 \\ -0.12x=-618 \\ x=(-618)/(-0.12) \\ x=5,150 \end{gathered}`

Finally, substitute the value of x into eq.1 to find the value of y