Chapter 1.7, Problem 10P

To determine

To calculate: Solve using the five step plan. Write out each step. A choice of possible numbers for one unknown is given.Western State College is 18 years older than Southern State. Western is also $2\frac{1}{2}$ times as old as Southern. How old is each? Choices for Southern State's age: 12, 14, 18.

Answer to Problem 10P

The age of Southern State is $a=12$ and the age of Western State is $a+18=12+18=30$

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, age of the Southern state and age of Western state.

Step 2: Let $a$ be the age of Southern State and $a+18$ be the age of Western State.

Step 3: As given, Western is also $2\frac{1}{2}$ times as old as Southern, such that $a+18=2.5a$ .

Step 4: Choices for $a$ are given as 12, 14, 18

$a$	$a+18=2.5a$	True / False
12	$12+18=2.5\left(12\right)$	True
14	$14+18=2.5\left(14\right)$	False
18	$18+18=2.5\left(18\right)$	False

From above table we can say that the age of Southern State is $a=12$ and the age of Western State is $a+18=12+18=30$

Step 5: Now we verify the answer

Western State is 18 years older than Southern State: $30-18=18$ , which is correct

Western State is 2.5 times as old as Southern State: $12\left(2.5\right)=30$ , which is also correct.