What this lesson covers
- per / each / every = a rate (multiply the variable)
- flat fee / one-time charge = a constant (add it)
- is / total = equals
- "less than" flips the order: 7 less than n is n - 7
Chapters
- 0:00Why word problems cost points
- 0:23Set up: define the variable
- 1:02Translate phrase by phrase, then solve
- 1:43The phrase-to-math dictionary
- 2:22Your turn
- 3:02Three traps
- 3:39Recap
Lesson transcript
The narration of the video, word for word, under its chapter headings.
0:00Why word problems cost points
Half of SAT math is word problems. And most points lost here aren't lost in the algebra. They're lost in the translation. One sentence, turned into the wrong equation. So let's turn English into math, phrase by phrase, until it's automatic.
0:23Set up: define the variable
Here's a typical one. A gym charges a thirty dollar signup fee, plus fifteen dollars per month. After how many months does the total cost hit one hundred eighty dollars? First move, always: define the variable. Let m be the number of months. Now every phrase in that sentence maps to one piece of an equation. Find the pieces.
1:02Translate phrase by phrase, then solve
Go phrase by phrase. Thirty dollar signup fee: that's a one-time amount, a constant, thirty. Fifteen dollars per month: the word per means multiply by the variable, fifteen m. Total cost is one hundred eighty: the word is means equals. Put it together: thirty plus fifteen m equals one hundred eighty. Now solve. Subtract thirty from both sides: fifteen m equals one hundred fifty. Divide by fifteen: m equals ten. Ten months.
1:43The phrase-to-math dictionary
Those phrases follow a fixed dictionary. Per, each, every: that's your rate, it multiplies the variable. A flat fee or one-time charge: that's the constant. The word is, or total, means equals. And watch this trap: less than flips the order. Seven less than a number is n minus seven, not seven minus n. Learn the dictionary once, and the translation stops being guesswork.
2:22Your turn
Your turn. A plumber charges seventy five dollars to show up, plus fifty dollars per hour. The bill came to three hundred twenty five dollars. How many hours? Define h as hours. Seventy five is the flat fee, the constant. Fifty per hour is fifty h. The bill is three hundred twenty five. So seventy five plus fifty h equals three hundred twenty five. Subtract seventy five: fifty h equals two hundred fifty. Divide: h equals five hours.
3:02Three traps
Three ways this goes wrong. One: flipping less than. Five less than x is x minus five. Order matters. Two: multiplying the one-time fee, when a signup or flat charge is a constant you add, not a rate. Three: solving for the wrong thing. The question asked for months, or hours, so answer that, not just x. Define the variable first and this trap disappears.
3:39Recap
So: define the variable, translate each phrase with the dictionary, then solve. The algebra was never the hard part. The translation was. Nail that, and word problems turn into easy points. Start free, and drill a set at satclimb.com. Keep climbing.
Read the written version: the Linear equations · one variable strategy guide, then try 25 hard Linear equations · one variable questions with full explanations. Both are free, no account needed.