At the first stop after a school bus left school, 4 children got off the bus. one quarter of the reamining children got off the bus at the second stop and 10 children got off at the third stop. if there were still 14 children on the bus after the third stop, how many children were on the bus as it left the school?
A) 28
B ) 32
C )34
D 35
E) 36
i did 10-(1/4-(x-4))=14 but it didnt give me the answer : /
charissa bought several packages of pencils from the collage bookstore. if each package contained either 5 or 12 pencils which of the following could not be the total number of oencils she bought?
At the first stop after a school bus left school, 4 children got off the bus. one quarter of the reamining children got off the bus at the second stop and 10 children got off at the third stop. if there were still 14 children on the bus after the third stop, how many children were on the bus as it left the school?
A) 28
B ) 32
C )34
D 35
E) 36
i did 10-(1/4-(x-4))=14 but it didnt give me the answer : /
Work backwards.
14 on the bus at the end.
10 had gotten off, that’s 24 total.
1/4 of the kids got off, that means 24 was 3/4. So there were 32 kids on the bus.
4 got off, so there were originally 36.
charissa bought several packages of pencils from the collage bookstore. if each package contained either 5 or 12 pencils which of the following could not be the total number of oencils she bought?
A) 32
B ) 33
C ) 34
D ) 35
E ) 36
eliminate any answer that’s a multiple of 5 or 12, so choices d and e are out.
32 - 12 = 20, which is a multiple of 5. It’s out.
34 - 24 = 10, which is a multiple of 5, so it’s out.
By the Chicken McNugget theorem (yes, it has a name, look it up on AoPS), the largest number of pencils that cannot be bought is 5*12 - 5 - 12 = 43.
Since 43 - 5 - 5 = 33, it is impossible to buy 33 pencils, because if there was a way to buy 33 pencils, then we could also buy 43 pencils by adding two more 5-packs, a contradiction.
can someone solve this one too…
-when a customer uses the coupon above at the keys and strings music store,what is the greatest percent discount the customer can recieve on a purchase? 10$ off any purchase of 50 or more
The $10 off discount is going to get you the greatest percent off when it’s 50.
So after the coupon, you’d be paying 40 dollars, which is 1/5 off the original price.
You are making this into something algebraic when it is really just asking about the concept of a percentage. Let’s try thinking of it another way: A group of people have each won a different amount of money. Then, each gave $10 of their winnings to charity. They all gave the same AMOUNT. But who gave the biggest PERCENTAGE? If you won $100, then the $10 represents 1/10th of your winnings, or 10%. If you won $1000, then the $10 is only 1% of your winnings. If you won $20, then the $10 is half your winnings or 50%. The largest PERCENTAGE is that $10 out of the SMALLEST winnings.
Now in this problem, the smallest purchase that gets you the $10 is $50. So 10 out of 50 is the largest PERCENTAGE discount you can earn.
Then, it comes down to this: do you know how to find what percent $10 is out of $50? There are lots of ways to do this. The quickest is just know that 1/5 is 20%.
Slower method: divide 1 by 5, and then multiply by 100
An even slower method for students who are shaky at percents: set up the ratios “is/of” = “percent/100”
You get 10/50 = x/100 which you can cross multiply and divide.
@pckeller Eh, I just find it easier to think in algebra. The recommended technique to solving wordy problems in my country is to reduce to problem to algebraic expressions. Then, you’ll only have to solve the equations or inequations. My teachers said that the technique would help reduce stupid mistakes made due to not reading the whole question.
Either solution is correct - but one possible problem with purely algebraic solutions is that you might accidentally translate the problem into the wrong equation. Even if you solve it correctly, your answer could be incorrect.
The most intuitive way for me is, $10 off $50 is a 20% discount, and whenever the price before discount increases, the percent discount decreases. So 20% is the answer.
More formally, letting x be the price before discount, the percent discount is (10/x)*100 = 1000/x, which is strictly decreasing in x.
Okidoki, I will throw in my two cents, despite thinking that this problem should not create a huge roadblock for anyone.
The question is
I will leave the straight algebra on the side as it has been covered. I will, however, add a tip which helps in most similar problems. Here is comes … when you see a problem with % … immediately look to rely on multiples of 100!
What is the percent discount the customer receives when he gets a rebate of $20 on a purchase of $100 or
What is the discount rate of 20 per 100? Say the sentence and you have the answer!
