Speed< > to change
Math · 09 · Algebra

Word Problems

Notes

Key points

  • Define the variable with units: “x = number of hours”.
  • Fixed + rate × quantity: C=50+12hC=50+12h.
  • “is” → =, “of” → ×, “per” → ÷, “more than” → +.
  • “5 less than xx” is x−5x-5, not 5−x5-x.
  • Two unknowns, two facts → a system (count equation + value equation).
  • Re-read: total or each? Hours or minutes? Whole number?

Formulas

Linear modely=mx+by=mx+bm = rate, b = starting value
Count and value systemx+y=Npx+qy=Tx+y=N\qquad px+qy=TTickets, coins, mixtures
Distanced=rtd=rt

Common traps

  • Reversing “less than”: 3 less than twice x is 2x − 3.
  • Mixing units in one equation (minutes with hours, cents with dollars).
  • Stopping at x when the question asks for the total cost.

SAT tip

Translate one phrase at a time. On multiple choice, test a simple number against every condition in the story.

Test yourself

10 official SAT questions on Word Problems, easiest first.

    Next lesson10 · Interpretation and Representation