Q 125 - Intermediate Algebra

Question

Write a uniform motion problem similar to Example $4.15$ that relates to where you live with your friends or family members. Then translate to a system

of equations and solve it.

Step-by-Step Solution

Answer

The first equation is $\$3000+\$120x$

The second equation is $\$4500+\$90x$

The solution of the equations are $x=50$

 

Step 1. Form the first equation

Suppose John spends $\$3000$ for a hotel and pays $\$120$ per night.

Let the number of nights spent in the hotel be $x$.

So total expenditure of John is given as:

$\$3000+\$120x$

Step 2. Form the second equation

Suppose Peter spends$\$4500$ for a hotel and then pays $\$90$ per night.

Let the number of nights spent in the hotels are $x$.

So total expenditure of Peter is $\$4500+\$90x$.

Step 3. Solve the equations

We know that the expenditure of John and Peter are the same.

So,

$\$3000+\$120x=\$4500+\$90x$

Subtracting $\$90$ from both sides we get:

$$\begin{gathered} \$3000+\$120x-\$90x=\$4500+\$90x-\$90x \\ \$3000+\$30x=\$4500 \end{gathered}$$

Subtracting $\$3000$ from both sides, we get:

$$\begin{gathered} \$3000+\$30x-\$3000=\$4500-\$3000 \\ \$30x=\$1500 \end{gathered}$$

Step 4. Find the value of x

Dividing both sides by $\$30$ we get:

$$\begin{gathered} \frac{\$30x}{\$30}=\frac{\$1500}{\$30} \\ x=50 \end{gathered}$$

The number of days spent by both John and Peter in a hotel is $50$ days