Problem 42
Question
Things did not go quite as planned. You invested \(\$ 12,000,\) part of it in stock that paid \(14 \%\) annual interest. However, the rest of the money suffered a \(6 \%\) loss. If the total annual income from both investments was \(\$ 680,\) how much was invested at each rate?
Step-by-Step Solution
Verified Answer
So, $7000 was invested at a 14% profit and $5000 suffered a 6% loss.
1Step 1: Setup the equation
We set up the equation using the given conditions from the problem, let \(x\) be the amount of money invested at 14% and the rest which is \(12000 - x\) suffered a 6% loss. So the equation will be \(0.14x - 0.06(12000 - x)= 680\) where 0.14 and 0.06 represent the 14% profit and 6% loss respectively.
2Step 2: Simplify the equation
We expand and simplify the equation by multiplying through the brackets, resulting in \(0.14x - 720 + 0.06x = 680\). This simplifies further to \(0.20x = 1400\).
3Step 3: Solve the equation
Solving for \(x\) gives us \(x = 7000\), which represents the amount invested at 14%.
4Step 4: Find the amount at a 6% loss
We are given that the total investment was $12000. Thus, the rest of the money, which is \(12000 - 7000 = 5000\), suffered a 6% loss
Other exercises in this chapter
Problem 41
Solve each equation by making an appropriate substitution. $$x^{4}-5 x^{2}+4-0$$
View solution Problem 42
Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(\frac{3 x}{10}+1 \geq \frac{1}{5}-\frac{
View solution Problem 42
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$x^{2}-9 x$$
View solution Problem 42
Perform the indicated operations and write the result in standard form. $$ \sqrt{-12}(\sqrt{-4}-\sqrt{2}) $$
View solution