ACT Math: Translate Word Problems into Equations Accurately

Word problem errors often occur during the translation step, not the math. Students misread "Maria spent twice as much as John" and set up the wrong equation. The solution is building a personal glossary of common phrases and their algebraic equivalents. "Twice as much as" means multiply by 2 (Maria=2×John). "Per" or "each" means division or rate (miles per gallon=miles/gallon). "Total" means sum (total cost=cost A+cost B). "More than" means addition (3 more than x means x+3, not 3+x, though order doesn't matter for addition). "Less than" means subtraction (5 less than y means y-5, not 5-y; order matters here). "Is" or "equals" means the = sign. Translate phrase-by-phrase, left to right, and use a variable to represent unknowns consistently.

Example: "John has 5 more apples than Maria. Together they have 25 apples." Translate: John=Maria+5 and John+Maria=25. Substitute: (Maria+5)+Maria=25, so 2×Maria+5=25, so Maria=10. Check: Maria=10, John=15, total=25. Correct.

Trap 1: Misreading "less than" or "more than" direction. "5 less than x" is x-5, not 5-x. Trap 2: Confusing "times as much" with "more times." "3 times as much" means multiply by 3. "3 times more" can ambiguously mean 3× or 4× (original plus 3 times more). Stick to the clearer phrasing. Trap 3: Forgetting units in a setup (dollars vs. cents, hours vs. minutes). "Sarah earns $12 per hour and works 8 hours" becomes 12×8=96 dollars, not hours. Trap 4: Setting up a rate incorrectly. "If a car travels 60 miles per hour, how far in 3 hours?" Distance=60 miles/hour × 3 hours=180 miles. Forget to include units and you might write 60+3=63 (wrong). Trap 5: Not defining variables clearly. If x is "Maria's apples," write it down. Ambiguity later causes errors. Always write: "Let x= [explicit definition]" at the start.

Slow-down move: Read the problem once, then write a one-sentence summary in plain English before translating to algebra.

Problem 1: "A book costs $4 more than a pen. Three pens and two books cost $31. Find the cost of one book." Let p=pen cost. Book=p+4. Equation: 3p+2(p+4)=31. Solve: 3p+2p+8=31, 5p=23, p=4.6. Book=8.6. Check: 3(4.6)+2(8.6)=13.8+17.2=31. ✓ Problem 2: "A worker makes $15 per hour. She worked 40 hours last week. How much did she earn?" Earnings=15×40=600. Problem 3: "The ratio of boys to girls is 3:2. If there are 15 boys, how many girls?" 3:2 means boys/girls=3/2. So 15/g=3/2. Cross-multiply: 3g=30, g=10. For each problem, write your variable definition and equation before solving.

If you miss any, redo the translation step slowly. Most mistakes happen there, not in arithmetic.

About 40% of ACT Math questions involve word problems. Students who translate accurately solve them in 1-2 minutes; those who misread spend 5+ minutes or get wrong answers. The translation skill is independent of math difficulty; a simple arithmetic problem translated wrong yields zero points. Sharpening your translation skill unlocks points that don't require advanced concepts.

This week, translate 10 word problems without solving. Check your equations against the original wording. Once you trust your translations, solving is fast.