What this lesson covers
is wrong, because the two percents are taken on different bases. The discount
came off the ORIGINAL price, which is the one number the question does not give
you. Name it x, write 0.70x = 63, and divide.
- Why the sale price is not the base
- The one equation: you paid 70%, so x = 63 / 0.70 = 90
- Every choice pushed back through the SAME check: candidate x 0.70 has to land on 63
- Why $81.90, $93 and $210 each come from a specific, nameable slip
- The three traps and the one-multiplication sanity check
- A percent off is always taken off the ORIGINAL, never off the sale price
- If p% came off, you paid (100 - p)%, so divide by that decimal
- A 30% cut and a 30% raise land on different bases and never cancel
- Your original must be bigger than the sale price, and one multiplication tests any choice
Chapters
- 0:00Intro
- 0:04A discount you have to undo
- 0:14The item, and four believable answers
- 0:32You paid 70%, so divide by 0.70
- 0:54Every choice through the same check
- 1:23Three traps
- 1:57Recap
Lesson transcript
The narration of the video, word for word, under its chapter headings.
0:14The item, and four believable answers
A jacket is on sale for sixty three dollars after a thirty percent discount. What was the original price? The discount came off a number you do not have yet, so sixty three is not the base. Every wrong answer on this page treats it like the base.
0:32You paid 70%, so divide by 0.70
Name the original price x. Thirty percent came off, so you paid seventy percent of it. That is zero point seven times x, and it equals sixty three. Divide both sides by zero point seven, and x is ninety. Check it. Thirty percent of ninety is twenty seven, and ninety minus twenty seven is sixty three.
0:54Every choice through the same check
Now run the tempting one back through the same check. Adding thirty percent onto sixty three gives eighty one ninety. Take thirty percent off eighty one ninety and you land on fifty seven thirty three, not sixty three. Mismatch. Ninety three, from adding thirty dollars, gives sixty five ten. Mismatch. Two hundred ten, from dividing by zero point three, gives one hundred forty seven. Mismatch. Only ninety comes back to sixty three.
1:23Three traps
Three traps. One, adding the percent back on. A thirty percent cut and a thirty percent raise are taken on different bases, so they never cancel. Two, reading the percent as dollars. Thirty percent of ninety is twenty seven, not thirty. Three, dividing by the piece that left instead of the piece that stayed. Zero point three is the discount. Zero point seven is what you actually paid. The fast check. Your original has to be bigger than the sale price, and every choice can be tested with one multiplication.
1:57Recap
You paid seventy percent, so divide by zero point seven. Percent off always comes off the original.
Read the written version: the Percentages strategy guide, then try 25 hard Percentages questions with full explanations. Both are free, no account needed.