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.

Short answer

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

The second equation is$\$4500+\$90x$

The solution of the equations are$x=50$

Step-by-step solution

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