Word Problems in Algebra
Most algebra on the test isn't 'solve for x' — it's a sentence about pens, ages, or money that YOU have to turn into an equation first. Master that translation and a huge chunk of the math section opens up.
| Phrase | Operation | Example |
|---|---|---|
| is, equals | = | 'x is 10' → x = 10 |
| of | × (multiply) | 'half of x' → 0.5x |
| per, each | rate × amount | '$4 each' → 4x |
| more than, sum | + | '3 more than x' → x + 3 |
| less than, fewer | − (flip order) | '5 less than x' → x − 5 |
Common signal words and the operations they map to.
Pens cost 48?
Enter a whole number, fraction (e.g. 3/4), or decimal (e.g. .75).
Worked examples
A taxi charges a flat fee of $3 plus $2 for each mile driven. If a ride costs $17 total, how many miles was the ride?
Maria is 4 years younger than twice her brother's age. If Maria is 18, how old is her brother?
A store sells notebooks for $3 each and pens for $1 each. Jordan buys some notebooks and 5 pens, spending $26 in total. How many notebooks did Jordan buy?
Common pitfalls
"5 less than x" is x − 5, never 5 − x. The phrase tells you to start with x and subtract. Slow down on any 'less than' wording and write the bigger quantity first.
The test often asks for a final quantity (the price, the total, or x + 2) after you solve for x. Re-read the last sentence of the problem and make sure your number matches what's actually requested.
Skipping the 'Let x = ...' step leads to mixing up which number is which, especially in two-person age or two-item cost problems. Always label your unknown in words first.
When a number is given outright (like '5 pens'), it's a constant, not a variable term. Multiply it out to a plain number and add it in — don't accidentally make it part of the variable expression.
Key takeaways
Always start by writing 'Let [variable] = [the unknown]' in plain words.
Translate signal words: 'is' → =, 'of' → ×, 'per/each' → rate, 'more/less than' → +/−.
Total cost = (price each) × (number of items), plus any flat fee.
'Less than' and 'younger than' subtract from the term BEFORE them — order matters.
After solving, re-read the question to answer exactly what's asked.
Further reading
Try it yourself
5 practice questions on Word Problems in Algebra, drawn from the question bank. The tutor is one click away if you get stuck.