Grade 9 Algebra Word Problems


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.




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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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