SOLVING EQUATIONS – WORD PROBLEMS
There are a few rules to remember when writing Algebra equations:
NOTES 4
1. First, you want to identify the unknown, which is your variable. What are you trying to solve
for? Identify the variable: Use the statement, Let x = _____. You can replace the x with
whatever variable you are using.
2. Look for key words that will help you write the equation. Highlight the key words and write an
equation to match the problem.
3. The following key words will help you write equations for Algebra word problems:
 more than - means add
 less than - means subtract
 times as many - means multiply
 "per" - means multiply
AGE PROBLEMS INVOLVING ONE PERSON :
Five years ago, John’s age was half of the age he will be in 8 years. How old is he now?
A)
B)
C)
D)
E)
F)
Define “x”
Look at the question again and put relevant expressions above it.
Write out the equation
Solve the equation
Answer the question
Check your answer to see if it works.
a) So, we will let x = John’s age
x-5
=
½
x+8
b) Five years ago, John’s age was half of the age he will be in 8 years. How old is he now?
(hint: when you see the words “was”, “will be”, “is” – these mean equal signs)
c) Write out the equation:
1
𝑥 − 5 = 2 (𝑥 + 8)
d) Solve the equation
e) Answer the question (this means to write it in a sentence)
f) Check your answer.
SOLVING EQUATIONS – WORD PROBLEMS
AGE PROBLEMS INVOLVING MORE THAN ONE PERSON:
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John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, John will be three
times as old as Alice. How old is Peter now?
A) Set up a table.
age now
age in 5 yrs
John
Peter
Alice
B) Define the variable ‘x’
C) Fill in the table with information given in the question.
John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, John will be three
times as old as Alice. How old is Peter now?
Let x be Peter’s age now. Add 5 to get the ages in 5 yrs.
John
Peter
Alice
age now
2x
x
x–5
age in 5 yrs
2x + 5
x+5
x–5+5
D) Write the new relationship in an equation using the ages in 5 yrs.
In 5 years, John will be three times as old as Alice.
2x + 5 = 3(x – 5 + 5)
E) Solve the equation
2x + 5 = 3(x – 5 + 5)
2x + 5 = 3x
x=5
F) Answer the question (in a complete sentence)
Peter is now 5 years old.
G) Check your answer to see if it works.
SOLVING EQUATIONS – WORD PROBLEMS
NOTES 4
MONEY PROBLEMS:
Joanne has $24 in her piggy bank in quarters, loonies and toonies. She has two fewer toonies than
loonies and twice as many quarters as loonies. How many coins of each type does she have?
A)
B)
C)
D)
E)
F)
Define “x”
Look at the question again and put relevant expressions above it.
Write out the equation
Solve the equation
Answer the question
Check your answer to see if it works.
SOLVING EQUATIONS – WORD PROBLEMS
OTHER TYPES OF WORD PROBLEMS
NOTES 4
 When 6 is added to four times a number, the result is 50. Find the number.
 The sum of a number and 9 is multiplied by -2 and the answer is -8. Find the number.
SOLVING EQUATIONS – WORD PROBLEMS
NOTES 4
 The length of a rectangular map is 15 inches and the perimeter is 50 inches. Find the width.
 Karin’s mom runs a dairy farm. Last year Betty the cow gave 375 gallons less than twice the
amount from Bessie the cow. Together, Betty and Bessie produced 1464 gallons of milk. How
many gallons did each cow give?