Question

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.

Laurie has \($46,000$invested in stocks and bonds. The amount invested in stocks is \)$8,000$ less than three times the amount invested in bonds. How much does Laurie have invested in bonds?

Short answer

Laurie invested $\$18,000$in bonds.

Step-by-step solution

Step 1. Given Information 

We are given that Laurie invested $\$46,000$in stocks and bonds.

We have to find the amount Laurie have invested in bonds.

Step 2. Forming the equation 

Let the amount invested in bonds be x,

We know that the amount invested in stocks is $\$8,000$less than three times the amount invested in bonds.

So, the equation will be,

$3x-8000=46000$

Step 3. Solving the equation 

Adding $8000$on both sides, we get

$$\begin{gathered} 3x-8000=46000 \\ 3x=46000+8000 \\ 3x=54000 \end{gathered}$$

Dividing by $3$, we get

$$\begin{gathered} x=\frac{54000}{3} \\ x=\$18000 \end{gathered}$$

Laurie invested$\$18000$in bonds.

Step 4. Checking the solution 

Putting the value of xin the equation, we get

$$\begin{gathered} 3x-8000=46000 \\ 3\left(18000\right)-8000=46000 \\ 54000-8000=46000 \\ 46000=46000 \\ LHS=RHS \end{gathered}$$

Hence the solution is correct.