Math Made Simple

Algebra Word Problems: Strategies for Success

Turn everyday language into equations with a clear process that works for school, homework, and real-life math.

The big idea

An algebra word problem gives you information in sentences. Your job is to define an unknown, translate the important relationships into math, solve the equation, and check whether the answer makes sense in the original story.

The five-step strategy

Define → Translate → Equation → Solve → Check

On a small phone screen, swipe horizontally inside the strategy box if it feels wide.

1. Define. Let a variable represent the unknown quantity.
2. Translate. Replace words with operations and relationships.
3. Write an equation. Make both sides describe the same quantity.
4. Solve. Use inverse operations to isolate the variable.
5. Check. Substitute the answer into the original situation and include units.

Common translation clues

Words	Math meaning	Example
sum, total, altogether	addition	x + 8
difference, fewer than	subtraction	x − 5
of, groups of, times	multiplication	3x
per, shared equally	division or a rate	d ÷ 4

On a small phone screen, swipe horizontally inside the table to view every column.

Worked examples

Example 1: An age problem

Story: Mia is 4 years older than Leo. Their ages add up to 26. How old is each person?

Define: Let Leo’s age be x. Mia’s age is x + 4.

x + (x + 4) = 26 → 2x + 4 = 26 → 2x = 22 → x = 11

Answer: Leo is 11 years old and Mia is 15 years old. Check: 11 + 15 = 26 and 15 − 11 = 4.

Example 2: A rectangle problem

Story: A rectangle is 3 feet longer than it is wide. Its perimeter is 30 feet. Find its dimensions.

Define: Let the width be w feet. The length is w + 3 feet. Perimeter means 2 × length + 2 × width.

2(w + 3) + 2w = 30 → 4w + 6 = 30 → 4w = 24 → w = 6

Answer: The width is 6 feet and the length is 9 feet. Check: 2 × 9 + 2 × 6 = 18 + 12 = 30 feet.

Example 3: Consecutive integers

Story: The sum of two consecutive positive integers is 41. Find the integers.

Define: Let the first integer be x. The next consecutive integer is x + 1.

x + (x + 1) = 41 → 2x + 1 = 41 → 2x = 40 → x = 20

Answer: The integers are 20 and 21. Check: 20 + 21 = 41.

Example 4: A ticket system

Story: An event sells adult tickets for $12 and child tickets for $8. Seven tickets bring in $72. How many of each ticket were sold?

Define: Let a be the number of adult tickets. Then the number of child tickets is 7 − a.

12a + 8(7 − a) = 72 → 4a + 56 = 72 → 4a = 16 → a = 4

Answer: Four adult tickets and three child tickets were sold. Check: 4 × $12 + 3 × $8 = $48 + $24 = $72.

A formula that helps

For a constant-rate situation, use:

amount = rate × time

For example, traveling 60 miles per hour for 2.5 hours gives 60 × 2.5 = 150 miles. Always keep the units attached so you can see whether the answer is reasonable.

On a small phone screen, swipe horizontally inside the formula box if needed.

Memory tip

“Name it, translate it, test it.” Name the unknown with a variable, translate the story into an equation, and test the final answer in the original sentence. If the answer does not fit the words or units, revisit the equation.

Common mistakes to avoid

• Do not assign a variable before deciding exactly what it represents.
• Watch comparison phrases. “5 fewer than x” means x − 5, while “5 more than x” means x + 5.
• Do not mix units. Convert minutes to hours or cents to dollars when the equation requires it.
• Do not stop after solving. Check the result in the original story.
• Reject impossible answers, such as a negative number of tickets or a rectangle with a negative width.

Practice questions

Define a variable, write an equation, solve it, and check your answer.

1. A number plus 9 is 27. What is the number?
2. A number is 6 less than another number. Their sum is 34. Find both numbers.
3. A rectangle is 5 inches longer than its width. Its perimeter is 34 inches. Find its dimensions.
4. A taxi charges a $4 starting fee plus $2 per mile. A ride costs $22 before tip. How many miles was the ride?
5. Three times a number, increased by 4, is 25. Find the number.

Answers

1. 18. Equation: x + 9 = 27, so x = 18.
2. 20 and 14. Let the larger number be x; then x + (x − 6) = 34, so 2x = 40 and x = 20. The smaller number is 14.
3. Width 6 inches and length 11 inches. Equation: 2(w + 5) + 2w = 34, so 4w + 10 = 34 and w = 6.
4. 9 miles. Equation: 4 + 2m = 22, so 2m = 18 and m = 9.
5. 7. Equation: 3x + 4 = 25, so 3x = 21 and x = 7.

Final takeaway

Algebra word problems become manageable when you slow down and follow the same routine: define the unknown, translate the language, write an equation, solve it, and check the result with units and context. The equation is not a guess; it is a compact description of the story.