Chapter 1.7, Problem 5P

To determine

To calculate: Solve using the five-step plan. Write out each step. A choice of possible numbers for one unknown is given.A bus went 318 km farther than a car. The car went one third as far as the bus. How far the car's distance: 147, 151, 159

Answer to Problem 5P

The distance car travelled is $a=159$ and the distance bus travelled is $159+318=159*3=477$

Explanation of Solution

Given information:A bus went 318 km farther than a car and the car went one third as far as the bus.

Calculation:

Step 1: Here we have two unknowns, distance travelled by the car and distance travelled by the bus.

Step 2: Let $a$ be the distance travelled by the car and $a+318$ be the distance travelled by the bus.

Step 3: As given, the car went one third as far as the bus such that $a=318=3a$ .

Step 4: Choices for $a$ are given as 147, 151, 159.

$a$	$a+318=3\left(a\right)$	True / False
147	$147+318=3\left(147\right)$	False
151	$151+318=3\left(151\right)$	False
159	$151+318=3\left(159\right)$	True

From above table we can say that the distance car travelled is $a=159$ and the distance bus travelled is $159+318=159*3=477$

Step 5: Now we verify the answer

The bus travelled 318 km farther than the car: $477-159=318$ , which is correct

The car went one third as far as the bus: $\frac{1}{3}\left(477\right)=159$ , which is also correct.