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Chapter 4: Q 125 (page 406)

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

of equations and solve it.

Short Answer

Expert verified

The first equation is $3000+$120x

The second equation is$4500+$90x

The solution of the equations arex=50

Step by step solution

01

Step 1. Form the first equation

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

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

So total expenditure of John is given as:

$3000+$120x

02

Step 2. Form the second equation

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

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

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

03

Step 3. Solve the equations

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

So,

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

Subtracting $90from both sides we get:

$3000+$120x-$90x=$4500+$90x-$90x$3000+$30x=$4500

Subtracting $3000from both sides, we get:

$3000+$30x-$3000=$4500-$3000$30x=$1500

04

Step 4. Find the value of x

Dividing both sides by $30we get:

$30x$30=$1500$30x=50

The number of days spent by both John and Peter in a hotel is50days

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