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These lessons cover grade 9 algebra word problems involving age, distance, rate, time and coins with examples and step-by-step solutions. It includes various examples and solutions for algebra word problems that you will commonly encounter in 9th grade.
Algebra Word Problems | ||
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Age Word Problems | Rate, Distance, Time Problems | Coin Word Problems |
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Words to Equations
Algebra Word Problems
Angle Word Problems (6th Grade)
Angle Word Problems (7th Grade)
Word Problems (Multiplication & Division)
2-Step Word Problems (Multiply/Divide/Add/Subtract)
Multi-step Word Problems (using +, -, ×)
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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