Heart of Algebra

Word Problems

Lost in translation? Learn how the SAT disguises simple algebra as complex English paragraphs.

The Secret Language of the SAT

Before you try to solve a word problem, you have to decode it. In standard form (\(y = mx + b\)), the SAT explicitly uses certain vocabulary to denote the slope \(m\) and the y-intercept \(b\).

Translating Slope (\(m\))

Slope represents a Rate of Change. It happens repeatedly. Look for magic multiplier words.
"He earns $15 per hour."
Rate = 15
"The pool drains 5 gallons each minute."
Rate = -5
"The tree grows 2 inches every day."
Rate = +2

Translating Y-Intercept (\(b\))

The y-intercept represents the Starting Amount. It happens exactly once. Look for flat fees or starting values.
"There is a $50 flat fee."
Constant = 50
"She started with 40 apples."
Constant = 40
"An initial deposit of $100."
Constant = 100

Putting It Together

The "Cell Phone Bill" Setup

"A phone company charges a $30 monthly fee plus $0.10 per text message sent."

Identify the parts:

  • The "monthly fee" happens once per month (regardless of usage). That's our starting amount (\(b = 30\)).
  • The word "per" tells us $0.10 is the rate attached to the changing variable (\(m = 0.1\)).
Cost = 0.1x + 30