Math 7 · Unit 2, Lesson 6: More Than One Change · Tile 3 of 3

The Surprise

Up 10 percent, then down 10 percent

Finn reads this

Here is the one that fools almost everyone the first time. Guess first, then work it out.

Predict, then check

Finn reads this
$100 × 1.10 = $110$110 × 0.90 = $99

It lands at $99, not $100, because the second 10 percent was taken from $110, not from $100. Ten percent of $110 is $11.

Two discounts are not one big discount

Elle reads this

20 percent off, then another 10 percent off, is not 30 percent off. A $50 game at 20 percent off is $40. Then 10 percent off $40 is $4 off, which leaves $36. From $50 to $36 is $14 off, and 14 out of 50 is 28 percent. Two discounts stack to 28 percent off, not 30.

$50 × 0.80 = $40$40 × 0.90 = $361450 = 28% off, not 30%
ElleMath-speak

Percent changes do not simply add, because each one is taken from a different whole.

FinnPlain English

The second percent is a percent of a new number, so you cannot just add them up.

Let me try a few

NC standards: NC.7.RP.3.

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