ACT Math: Translate English Sentences into Algebra Instantly

Word problems require you to convert English into equations. Learn these conversions: "is" or "equals" means =. "More than" means +. "Less than" means -. "Times" or "of" means ×. "Divided by" means /. "A number" or "some amount" means a variable (x, y, etc.). Example: "Five more than twice a number is 17." Translation: 2x+5=17. Memorize these conversions and you can set up 90% of word problems in 30 seconds, leaving time for solving.

More examples: "A number decreased by 3 equals 10" translates to x-3=10. "The product of two consecutive integers is 42" translates to x(x+1)=42. "Three times the sum of a number and 5" translates to 3(x+5). Consecutive integers are x and x+1. Consecutive even/odd integers are x and x+2. Ages are x and x+10 (for 10-year difference), etc. Building a "vocabulary" of these patterns lets you translate any word problem.

Trap 1: "Less than" and "more than" are backwards in equations. "5 less than x" is x-5, not 5-x. Trap 2: Reading "per" as a single operation when it often requires multiple steps. "Miles per hour" is miles/hours (a rate). "People per team" is total people/number of teams. Trap 3: Misidentifying what variable represents. If "x is the larger number," stick with that throughout; do not switch mid-problem. Write your variable definition clearly at the start: "Let x=the smaller number. Then x+2=the larger number." This prevents mid-problem confusion.

Example: "A store sells pens for $2 each. How many pens can you buy with $15?" Let x=number of pens. Equation: 2x=15, so x=7.5. You can buy 7 pens (not 7.5, since you cannot buy half a pen). This clarifies why defining your variable precisely matters.

Sentence 1: "A number plus 8 equals 20." Sentence 2: "Five less than twice a number is 13." Sentence 3: "The product of two consecutive integers is 56." Sentence 4: "Sarah has $5 more than Tom." Sentence 5: "A car travels 60 miles per hour." Sentence 6: "The sum of three consecutive integers is 30." Sentence 7: "John is 3 times as old as his son." Sentence 8: "A rectangle's length is twice its width." Sentence 9: "The price after a 20% discount is $40." Sentence 10: "If 40% of the class passed, 60 students passed." For each, write an equation without solving. Do this drill twice this week; translation speed improves faster than any other test-day skill.

Answers: 1) x+8=20. 2) 2x-5=13. 3) x(x+1)=56. 4) x=Tom's money, Sarah's=x+5. 5) d/t=60 or d=60t. 6) x+(x+1)+(x+2)=30. 7) John's age=3×son's age, or x=3y. 8) L=2W. 9) 0.8p=40 (price after 20% off). 10) 0.4T=60.

Word problems intimidate many students, but 80% of the difficulty is translation, not solving. Once you convert English to an equation, the algebra is usually straightforward. Mastering translation takes 30 minutes of focused practice and pays dividends because word problem competency transfers across topics: algebra, rate, percentage, and geometry word problems all use the same translation principles.

Commit to the ten-sentence drill this week. By test day, you will convert words to equations faster than you read the question, giving you time to solve and check.