Translating Word Problems into Algebra
Practice the 4-step translation routine, the English-to-algebra dictionary, and the classic PSAT traps.
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Questions Covered in This Set
10 cards to master
What are the 4 steps of the translation routine?
1) Name the unknown (with units), 2) underline number-words and relationship words, 3) translate phrase by phrase, 4) check by plugging in an easy number.
Why is 'Let m = the number of months' so important?
It forces you to decide exactly what the variable counts, which prevents most translation mistakes.
Translate: '5 less than x'
x − 5 (NOT 5 − x — English reverses the order here)
Difference between 'twice the sum of x and 3' and 'twice x, plus 3'
2(x + 3) vs. 2x + 3 — the word 'sum' creates a package that needs parentheses.
'Three less than four times a number is 29.' Write and solve.
4n − 3 = 29 → 4n = 32 → n = 8
A phone plan costs $25 per month plus $0.10 per text. Write cost C for t texts.
C = 0.10t + 25 (check: 0 texts → $25)
Maria has 4 more than twice as many stickers as Jon; together 34. Set it up.
Let j = Jon's: j + (2j + 4) = 34 → 3j + 4 = 34 → j = 10, Maria 24.
When there are two unknowns, which one should be your variable?
The thing everything else is measured against — the choice that makes the other expression simplest.
In P(d) = 1200 − 45d (pages remaining after d days), what does 45 mean?
The number of pages read per day — the per-unit rate (m in y = mx + b).
Rectangle length is 3 cm less than twice width w. Perimeter?
L = 2w − 3, so P = 2(2w − 3) + 2w = 6w − 6
