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## SAT (Fall 2023)

### Course: SAT (Fall 2023) > Unit 10

Lesson 3: Problem solving and data analysis- Ratios, rates, and proportions — Basic example
- Ratios, rates, and proportions — Harder example
- Percents — Basic example
- Percents — Harder example
- Units — Basic example
- Units — Harder example
- Table data — Basic example
- Table data — Harder example
- Scatterplots — Basic example
- Scatterplots — Harder example
- Key features of graphs — Basic example
- Key features of graphs — Harder example
- Linear and exponential growth — Basic example
- Linear and exponential growth — Harder example
- Data inferences — Basic example
- Data inferences — Harder example
- Center, spread, and shape of distributions — Basic example
- Center, spread, and shape of distributions — Harder example
- Data collection and conclusions — Basic example
- Data collection and conclusions — Harder example

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# Percents — Harder example

Watch Sal work through a harder Percents problem.

## Want to join the conversation?

- bruh this is easier than the easy example(79 votes)
- How do people think this explanation is easy? Am I dumb?(44 votes)
- Ok so the initial cost is $40, and you get 30% off. This means you need to do 40(1-.3) because you want to find 30% off of 40, not 30% of 40. This gives you 40(.7) which is equal to 28. Now, to find the additional discount, you can do the final price divided by 28.

22.4/28 = 0.8

So now we know 22.4 (the final price) is 80% of the price with the discount (28). In other words, the second discount is 100-80 = 20%

I hope this made things clearer, though some might consider this problem easy, it's not easy for everyone - remember that at the end of the day everyone has their own strengths and weaknesses, and knowing these strengths and weaknesses will let you know what to work on and where to spend the most time on during the sat.

Lmk if you have any questions.(56 votes)

- To find the additional discount, why not just do :

(28 - 22.40) / 28 = 0.2 = 20%

Seems faster than the calculation shown in the example.(27 votes) - hahaha, This is very easy, easier than the basic example😅😅(20 votes)
- Wait . . .

Let the additional discount be x so,

[(30+x)/100]*40=22.4

then x comes out to be 26 hence the additional discount should be 26%

In order to check my above answer

30% + 26% = 56%

and 56% of $40 = $22.4 i.e the final price. . .

IF I'M WRONG PLZ LET ME KNOW HOW ?(8 votes)- There's one tiny detail that you may have overlooked. The additional discount is a percentage off of the sale price, not the actual price, as you have it in your equation. To do that, you would have to take the discounted price (.7 * 40) and apply the additional discount to that price: x * (.7*40). Set that equal to 22.4 and you would get a percent discount of .8, or 20% off.

(Forgot to mention this while writing the answer, but don't forget that the discounts are a percentage OFF, not just a percentage of the marked price. You'd then have to do 100 - the percent to find the discounted price (using 0.7 for 30% off instead of 0.3).(10 votes)

- What type of cereal did he have?(12 votes)
- Asking the real questions!(1 vote)

- Where is "Good luck! You've got this"? ;(((((11 votes)
- could you also use the difference/initial value method instead? I feel like it may be easier just to do the following:

5.6/22.40 x 100 which also gives you 20%

(I got the 5.6 by subtracting 22.4 from 28)(11 votes)- agreed, it's easier at least for me(1 vote)

- This one was so confusing. Is there another way you can do the jeans problem?(5 votes)
- 30 percent of 40 dollars is 12 , subtract it with 40 and we get 28 dollars. Now to find out the additional discount you can choose one from the options as 12 and 20 are smaller number since we only need to get 22.4 so now discount off both and when you do 20% you will get 5.6 which if you subtract will give you 22.4(7 votes)

- can we use calculator for this kind of question on test day?(4 votes)
- You can use a calculator for all of the questions in the Digital SAT.(8 votes)

## Video transcript

- [Instructor] A pair of
jeans that regularly costs $40 is on sale for 30% off. As part of a promotion, each
customer will also receive an additional discount
on the marked sale price at the cash register. If the final price of
the jeans was $22.40, what additional discount was applied to the marked sale price? All right, this is interesting and useful, 'cause we need to know what
we're gonna pay for our jeans. All right, so the regular price is $40, we're gonna assume
everything is in dollars. It's on sale for 30% off. Well if you're 30% off that means it's going to cost
70% of the regular price. So let's put 70% of 40, so
let's multiply that times 0.7, which is the same thing as 70%. 40 times 0.7, that's
going to be equal to $28, yeah seven times four is 28, .7 times 40 is also going to be 28. All right so it's gonna be
$28 would just be the 30% off, but the final price of
the jeans was 22.40. What additional discount was applied to the marked sale price? Well to figure that
out we can just divide. We can say well what
fraction of 28 is 22.40? 22.40 divided by, divided by 28. Well this is going to
be equal to, let's see, 28 and actually you could even rule out, I'll do the arithmetic right over here, so 28 goes into 22.40, so I'll get the decimal right over here, 28 doesn't go into 22,
but it does go into 224. Let's think about it, how many
times does 28 go into 224? I don't know, maybe seven
times, let's see if this works. So it goes seven times,
seven times eight is 56, seven times two is 14 plus five is 19. And then if we were to subtract, let's see we could make this
a 14 regrouped from here, this would be a one, but
then we remove from here, this would be an 11, 14 minus six is, 14 minus six is eight,
11 minus nine is two. Okay so we actually could
have gotten one more in there, so let's see, this is going to go, 28 goes into 224 exactly
eight times, eight times, eight times eight is 64, 64, eight times two is 16 plus
six is 22, no remainder. So this is 80% of the marked down price. So if this is 80%, if this is 80% of this, then the additional discount that was taken is going to be 20% because once you take 30%
off you'd expect to pay $28, but you only paid 80% of that, so they took off another 20%,
they took off another 20%. If you take off 20%, then you're going to pay 80% of the price.