Question

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

Marc just bought an SUV for \($54,000$. This is \)$7,400$ less than twice what his wife paid for her car last year. How much did his wife pay for her car?

Short answer

The price of Marc's wife car is $\$30,700$.

Step-by-step solution

Step 1. Given Information 

We are given that the price of Marc's car is $\$54,000$.

We have to find the price of his wife's car.

Step 2. Forming the equation 

Let the price of car of Marc's wife be x,

We know that the price of Marc's car is $\$7,400$less than twice of price of his wife's car.

So, the equation will be,

$2x-7400=54000$

Step 3. Solving the equation The total number of 

Adding $7400$on both sides, we get

role="math" $$\begin{gathered} 2x-7400=54000 \\ 2x=54000+7400 \\ 2x=61400 \end{gathered}$$

Dividin by $2$,

$$\begin{gathered} x=\frac{61400}{2} \\ x=\$30,700 \end{gathered}$$

Hence, the price of Marc's wife car is $\$30,700$.

Step 4. Checking the solution 

Putting the value of xin the equation, we get

$$\begin{gathered} 2x-7400=54000 \\ 2\left(30700\right)-7400=54000 \\ 61400-7400=54000 \\ 54000=54000 \\ LHS=RHS \end{gathered}$$

Hence the solution is correct.