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Algebra Word Problems

How to answer grade 9 algebra word problems involving age, distance, rate, time and coins with examples and step by step solutions? The following are some examples and solutions for algebra word problems that you will commonly encounter in grade 9.

**Grade 9 Algebra Word Problems**

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.

More Math Word Problems

Algebra Word Problems

How to answer grade 9 algebra word problems involving age, distance, rate, time and coins with examples and step by step solutions? The following are some examples and solutions for algebra word problems that you will commonly encounter in grade 9.

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.

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.

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?

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?

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?

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?

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.

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?

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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