Word Problems: Turning English Into Equations

Students rarely lose word-problem points because the algebra is hard. They lose them in the translation — misreading "less than," picking the wrong unknown, or skipping the check. The fix is a system. Every word problem, no matter the topic, yields to the same four steps: define the unknown, translate the sentence, solve, and verify. Run that system and the paragraph stops being scary.

This guide gives you the system, a keyword dictionary, the most common problem types, and worked and practice problems matched to real test difficulty at Northside Tutoring.

Why Word Problems Matter

The modern SAT and ACT are overwhelmingly word-based. Pure "solve for x" questions are rare; most problems wrap the math in a real-world story. Translation is therefore the highest-leverage math skill on the test — it determines whether you even set up the right equation.

The Four-Step System

1. Define the variable in plain words: "let x = the number of hours worked."
2. Translate the sentence phrase by phrase into an equation.
3. Solve the equation.
4. Check by re-reading the question and plugging the answer back in.

The Keyword Dictionary

Words	Operation
sum, increased by, more than, total	+
difference, decreased by, less than, fewer	−
product, of, times, twice, each	×
quotient, per, divided by, ratio	÷
is, was, equals, results in, gives	=

Defining the Right Variable

Let your variable stand for the quantity the question asks about, and express everything else in terms of it. "Maria is 3 years older than twice Tom's age" becomes M = 2T + 3. Choosing the smaller or simpler quantity as the base usually keeps the algebra cleanest.

Common Problem Types

• Consecutive integers: n, n + 1, n + 2 (or n, n + 2, n + 4 for evens/odds).
• Age problems: write expressions for "now" and "then," watching the time shift.
• Mixture / money: count value, not just quantity (e.g., 5¢ × nickels).
• Distance: distance = rate × time, one equation per traveler.

Checking Your Answer

The check is not optional — it's where you catch translation mistakes. Re-read the original sentence with your answer in place. If "the sum is 30" but your numbers add to 28, the setup was wrong. A ten-second check saves a missed question.

Where You'll See This — Test by Test

Word problems are the dominant format on the modern SAT and ACT, so the translation system pays off on nearly every question. The SSAT uses them heavily too. No reference sheet helps here — method is everything.

Watch the Lesson

Sometimes a diagram needs a voice. In the short video below, one of our Northside tutors walks through the core idea and works through test-style problems in real time.

Worked Example Problems

These problems are calibrated to the difficulty you'll actually see on test day. Try each one before opening the solution.

Common Mistakes to Avoid

Practice Problems — You Try

Three problems below. Work each before checking the solution.

The Northside Method — How We Teach This 1-on-1

Reading a blog is a great starting point. But there's a meaningful gap between understanding a concept and reflexively applying it under timed conditions. That gap is exactly what our tutors close.

Every Northside student works through a four-step framework:

1. Assessment. We diagnose which specific skills are slowing your student down — not just whether they "get it" in the abstract.
2. Perfect-match coach. We pair them with an elite tutor (we accept only the top 1% of applicants) whose teaching style fits how your student actually learns.
3. Bespoke plan. A roadmap built around your student's target score, target timeline, and current pacing data.
4. Data-driven adjustment. Every session ends with a check on whether the student's accuracy and speed are moving in the right direction.

And if a student meets all eligibility requirements but doesn't hit the defined score improvement? We provide 5 additional hours of cohort learning at no cost. That's the Northside guarantee — built on 25 years of measured outcomes.