Lesson 13 of 1524
Algebra
This chapter is the algebra the rest of the book actually uses.
Practice this chapterYou already solve ax + b = c and read y = mx + b. Here those skills translate word sentences: “12 is 30% of what number?”
The slope is still the coefficient of x, and the constant term is still the y-intercept. Percent sentences become equations before they become arithmetic.
A percent sentence
part = rate × whole
Identify which of the three numbers is missing, then solve.
Worked example
12 is 30% of what number?
- 1The sentence says the part is 12 and the rate is 30%. The whole is the unknown: part = rate × whole.
- 2Write 12 = 0.30 × n. The decimal 0.30 is 30/100, not 30.
- 3Divide both sides by 0.30: n = 12 / 0.30.
- 412 / 0.30 = 40.
- 5Check: 30% of 40 is 0.30 × 40 = 12. That matches the given part.
Result: 40
Why. The part is known and the whole is missing, so you divide the part by the rate. “30% of 12” would be the other sentence, 0.30 × 12 = 3.6, because there the whole is the 12.
“30% of 12” and “12 is 30% of what” are not the same question. The first answer is 3.6. The second is 40.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.