These lessons cover grade 9 algebra word problems involving age, distance, rate, time and coins with examples and step-by-step solutions? Includes various examples and solutions for algebra word problems that you will commonly encounter in grade 9.

**Related Pages**

Grade 8 Algebra Word Problems

Algebra Word Problems

Solving Equations

More Algebra Lessons

**Age Problems with two unknowns or variables**

**Example:**

Taylor is five times as old as Spenser. The sum of their ages is eighteen. How old are Taylor and Spencer?

**Solution:**

Let x represent Spenser’s age

Therefore, Taylor’s age is 5x

x + 5x = 18

6x = 18

x = 3

Therefore, Spenser is 3 years old and Taylor is 15 years old.

**Grade 9 Algebra Word Problems - Age**

**Example 1:**

A mother is three times as old as her daughter. Six years ago, the mother’s age was six tines that of her
daughter. How old are they now?

**Solution:**

Let x represent the daughter’s age.

Therefore, 3x is the mother’s age.

6(x - 6) = 3x - 6

6x - 6 = 3x - 6

3x = 30

x = 10

Therefore, the daughter’s is 10 years old and the mother is 30 years old.

**Example 2:**

A father is now three times as old as his son. Eight years ago, the father was five times as old as his son.
How old are they now?

**Grade 9 Algebra Word Problems - Rate, Distance, Time**

**Example:**

A bus leaves the terminal and averages 40 km/hr. One hour late, a second bus leaves the same terminal
and averages 50 km/hr. In how many hours will the second bus overtake the first?

**Grade 9 Rate, Distance, Time Word Problems**

**Example 1:**

One motorist travels 5 km.hr faster than another. They leave from the same place and travel in opposite directions.
What is the rate of each if they are 195 km apart after 3 hours?

**Example 2:**

A pilot flew from airport A to airport B at a rate of 100 km/hr and flew back from airport B to
airport A at 120 km/hr. The total time it took was 11 hours. How far is it from airport A to airport B?

**Grade 9 Algebra Word Problems - Coins**

**Example:**

A coin collection amounting to $25 consists of nickels and dimes. There are 3 times as many nickels and dimes.
There are 3 times as many nickels as dimes. How many coins of each kind are there?

**Solution:**

Let x = number of dimes

3x = number of nickels

10x + 5(3x) = 2500

25x = 2500

x = 100

Therefore, there are 100 dimes and 300 nickels.

**Grade 9 Coin Algebra Word Problems**

**Example:**

Mr. Rogers has $4.62. He has 3 times as many dimes as nickels and 6 more pennies than dimes. How many coins of
each kind does he have?

**Coin Algebra Word Problems - Grade 9**

**Example:**

Bob has in his pocket a number of pennies, 5 times as many nickels as pennies and 5 more quarters than pennies.
The coins amount to $2.27. Find the number of each kind of coin.

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