SAT Problem Solving Framework • Topic 1 of 4

Translating Word Problems

Translation converts English into algebra phrase by phrase. Define a variable for the unknown (“let x = the number”), then map keywords: “is” means =, “of” means ×, “more than” / “sum” means +, “less than” means − (and reverses order — “5 less than x” is x − 5), “per” means ÷, “twice” means 2×, “percent” means ÷ 100. Build the equation left to right from the sentence, then solve. The discipline is to write the equation before doing any arithmetic — most errors happen when students jump to numbers without a clear equation. Read the sentence twice: once for the story, once to translate.

✅ Solved examples

1. Translate: “5 more than twice a number is 17.”
2x + 5 = 17 → x = 6.
2. Translate: “7 less than a number is 12.”
x − 7 = 12 → x = 19.
3. Translate: “30% of a number is 24.”
0.30x = 24 → x = 80.
4. Translate: “the sum of x and 8 is three times x.”
x + 8 = 3x → x = 4.

✏️ Practice — try these, take hints as needed

1. Translate and solve: “4 more than a number is 11.”
x + 4 = 11.
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—
x = 7.
2. Translate and solve: “twice a number is 18.”
2x = 18.
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x = 9.
3. Translate: “6 less than a number” (as an expression).
Order reverses.
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x − 6.
4. Translate and solve: “20% of a number is 15.”
0.2x = 15.
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x = 75.
5. Translate and solve: “the sum of a number and 5 is 21.”
x + 5 = 21.
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—
x = 16.
Identifying Hidden Variables →