Word problems
Set up and solve one-variable equations from word problems, including two-step and geometry or consecutive integer problems.
Worked examples
Writing and solving a one-step word problem
Straightforward
Problem
A number is doubled and then 3 is added. The result is 11. Find the number.
1
Define a variable.
Let the unknown number be .
2
Write an equation from the word problem.
3
Subtract 3 from both sides.
4
Divide both sides by 2.
Answer
The number is .
Setting up and solving a two-step word problem
Moderate
Problem
A plumber charges a call-out fee plus per hour. A customer is charged in total. How many hours did the plumber work?
1
Define a variable.
Let = the number of hours worked.
2
Write an equation for the total charge.
3
Subtract 45 from both sides.
4
Divide both sides by 60.
Answer
The plumber worked hours.
Solving a geometry word problem using angle sums
Challenging
Problem
The three interior angles of a triangle are , and . Find the value of and state each angle.
1
Define the variable.
Let represent the smallest angle in degrees.
2
Use the angle sum of a triangle.
The interior angles of a triangle add to , so:
3
Collect like terms.
4
Divide both sides by 6.
5
State each angle.
, ,
Answer
. The three angles are , and .
Practise
Q1·Straightforward
A number is doubled and then 3 is added. The result is 11. Find the number.
Explanation
Let the number be . Then . Subtracting 3: . Dividing by 2: .
Q2·Straightforward
When 9 is added to three times a number, the result is 24. Find the number.
Explanation
Let the number be . Then . Subtracting 9: . Dividing by 3: .
Q3·Straightforward
A number is multiplied by 5 and then 7 is subtracted. The result is 18. Find the number.
Explanation
Let the number be . Then . Adding 7: . Dividing by 5: .
Q4·Straightforward
A number is divided by 4 and then 2 is added. The result is 8. Find the number.
Explanation
Let the number be . Then . Subtracting 2: . Multiplying by 4: .
Q5·Moderate
Mia buys 4 identical books and a bookmark costing . She pays in total. What is the cost, in dollars, of each book?
Explanation
Let = cost of one book in dollars. Then . Subtracting 3: . Dividing by 4: . Each book costs .
Q6·Moderate
Tom is 3 years older than twice his sister's age. Tom is 19 years old. How old is his sister?
Explanation
Let = sister's age. Then . Subtracting 3: . Dividing by 2: . His sister is 8 years old.
Q7·Moderate
A plumber charges a call-out fee plus per hour. A customer is charged in total. How many hours did the plumber work?
Explanation
Let = number of hours. Then . Subtracting 45: . Dividing by 60: . The plumber worked 3 hours.
Q8·Moderate
The perimeter of a rectangle is 40 cm. Its length is 6 cm more than its width. Find the width in centimetres.
Explanation
Let = width in cm. Length . Perimeter: , so , giving . Subtracting 12: . Dividing by 4: . The width is 7 cm.
Q9·Challenging
The three interior angles of a triangle are , and . Find the value of .
Explanation
The angle sum of a triangle is . So , giving . Dividing by 6: .
Q10·Challenging
Two consecutive even integers add to 94. Find the smaller integer.
Explanation
Let the smaller even integer be . Then , giving . Subtracting 2: . Dividing by 2: . The smaller integer is 46.
Q11·Challenging
The sum of three consecutive integers is 66. Find the largest integer.
Explanation
Let the smallest integer be . Then , giving . Subtracting 3: . Dividing by 3: . The largest integer is .
Q12·Challenging
A rectangle's length is 5 cm more than its width. Its perimeter is 46 cm. Find the length in centimetres.
Explanation
Let = width in cm. Length . Perimeter: , so , giving . Subtracting 10: . Dividing by 4: . Length cm.