Word Problems — Translating English to Math

GRE Quantitative · Axiom Academy

LESSON Word Problems — Translating English to Math Every word problem is really just a translation problem — learn the phrase-to-symbol key and you can turn any sentence into an equation you already know how to solve. Word problems reuse the same handful of phrases again and again. Learn what each one means in symbols, and reading a problem becomes mechanical: find the phrase, write the symbol, move on. 2. Define One Quantity, Express the Other When a problem relates two quantities, name the simpler one with a variable, then write the second one in terms of the first — never introduce two separate unknowns for one relationship. "Jane has 3 more apples than Tom. Together they have 15 apples. How many does each person have?" Let Tom's apples = t. Jane's apples = t + 3 (translate "3 more than"). "Together they have 15" translates to the equation. 3. Same Process, Any Problem Shape — Then Check The process from Steps 1–2 doesn't change with the topic. Rate-time-distance problems use one extra piece of vocabulary — distance = rate × time — but the translation is identical: name a variable, write each quantity in terms of it, and translate the sentence that ties them together into an equation. "Two cars start 260 miles apart and drive toward each other, one at 60 mph and the other at 70 mph. How long until they meet?" Car A: 60(2)=120 mi. Car B: 70(2)=140 mi. 120+140=260 ✓︎ — matches the gap, and 2 hours is a sensible amount of time.

This is the written version of the interactive lesson above. See the full GRE Quantitative course.