SAT word problems: translate English into equations step by step
Most word problems become easy once the equation is right. Learn the phrases that map to symbols, the “less than” trap, and how to interpret every number in a model.
The short version
What you'll take away
- Define each variable with its units before writing anything else.
- “5 less than x” is x − 5, not 5 − x. The order reverses.
- In a model like C = 40 + 25m, the constant is a one-time amount and the coefficient is a rate per unit.
In this article
Words that become symbols
See the skill
Phrase to symbol
is, equals, results in
=
“The total is 290” → … = 290
of, times, product
×
“Twice a number” → 2n
more than, increased by
+
“7 more than x” → x + 7
less than (order reverses!)
−
“5 less than x” → x − 5
A routine that works every time
See the skill
From words to an answer
Name the unknown
Let m be the number of months. Write the units next to the variable.
List the quantities
$40 sign-up fee (once), $25 per month, $290 total.
Find the relationship
One-time amount + rate × count = total: 40 + 25m = 290.
Solve and check
25m = 250, so m = 10. Check: 40 + 25(10) = 290, and 10 months is reasonable.
Interpret every number in a model
Your turn
Quick practice
The number of tickets sold, t, is 12 less than 3 times the number of programs sold, p. Which equation represents this relationship?
Hint: “12 less than [something]” means [something] − 12.
Practice: try these before checking the answers
- 1. Seven more than twice a number is 31. Find the number.
- 2. A taxi charges $3 plus $2.50 per mile. A ride costs $23. How many miles was it?
- 3. In \(\displaystyle C = 40 + 25m\), what does 40 represent?
- 4. A rectangle’s length is 3 more than its width, and its perimeter is 26. Find the length and width.
Sources & further reading
One step from here
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