Hi everyone,
Just thought that the marathon chain was getting a little too long, so I decided to continue it on this post.
Rules:
1. Look at the posted problem. If you know how to do it, solve it and post your solution, not just your answer.
2. After getting a confirmation that your solution is correct, you will be able to post your own problem for others to solve. (Only the first person with the correct solution will be eligible to post another problem.)
3. At any given time, only 1 problem should be "active".
4. The problem you post should be of your own challenge level.
5. Mention the problem number when you post a problem.
6. The marathon will run in this chain.
Enjoy!!!
Neha, please post your problem. We have just left off on problem 11, so yours will be problem 12.
ReplyDeleteProblem 12
ReplyDeleteMilk costs x cents per half-gallon and y cents per gallon. If a gallon of milk costs z cents less than 2 half-gallons, which of the following equations must be true?
(A) x - 2y + z = 0
(B) 2x - y + z = 0
(C) x - y - z = 0
(D) 2x - y - z = 0
(E) x + 2y - z = 0
(Posted on behalf of Auryan.)
This comment has been removed by the author.
ReplyDeleteHere's my problem:
ReplyDeleteThere were two candidates in the final round of an election. They split the votes by a ratio of 5:7. If a total of 18,000 votes were cast, how many of those did the loser get?
Oh! Agni, you already posted a problem?!?!
ReplyDeleteI didn't notice it until my page refreshed when I posted my problem. Which problem shall we use?
We'll go with Auryan's question for now.
ReplyDeleteNeha, the next time you are entitled to post a problem, please post it sooner.
You may delete your comment for now. Thanks!
I think it is (d)
ReplyDeleteVishal, please support your answer with an approach :)
ReplyDeleteMy answer is D.
ReplyDeleteCost of 1/2 gallon = x cents
1 gallon = y cents
1 gallon = z cents < 2 half-gallons
That means 1 gallon = z cents < 2x
Therefore 1 gallon = z cents = x
So, 2x - y - z = 0
Good job, Neha! You can post a different problem now, since your previous problem has already been exposed. (Remember to mention the problem number. It will be Problem 13.)
ReplyDeleteOk, I'm working on it. I'll post it soon!
ReplyDeletePROBLEM 13
ReplyDeleteThe pies in a bakery are apple or cherry. If the ratio of the number of apple pies to the number of cherry pies is 3:1, then which of the following cannot be the total number of pies?
(A) 26
(B) 32
(C) 44
(D) 52
(E) 64
For every 4 pies, 3 are apple and 1 is cherry. So the number of pies has to be a multiple of 4. 26 is not a multiple of 4 so the answer is (A).
ReplyDeleteGood job, Vishal. Go ahead and post your problem. It will be Problem 14. Please mention the problem number when you post.
ReplyDeleteI am thinking of a problem. It will be posted tonight
ReplyDeleteProblem 14
ReplyDeleteIf 4x + 2x + 10 = 28, then what is x*x.
PROBLEM 14 SOLUTION
ReplyDeletex*x is equal to 9.
Solution:
simplyfiy.....
6x = 18
x = 3
3 x 3 = 9
Good job, Maya. You may post a problem now.
ReplyDeletePROBLEM 15:
ReplyDeleteLilly is playing a computer game that lets her customize a story. There are 2 different eras and 5 locations to choose from. How many different stories can Lilly construct?
Hello?
ReplyDelete2 x 5 = 10
ReplyDelete10 different locations
Yay, Vishal! Finally someone took the lead!
ReplyDeleteYou may post a problem now. (Problem 16)
Problem 16
ReplyDeleteThe Star ferry is full when it carries 15 cars on board. The ferry is also full when it carries 9 trucks on board. The ferry cannot carry both types of vehicles at the same time. On a particular day, the ferry made 6 trips across the lake and carried a total of 78 vehicles If the ferry was full on each trip, how many cars did it carry altogether that day?
Agni, when are you going to tell us about the MATHCOUNTS results?
ReplyDeleteMr. Pearson is grading the test. You'll probably know the results by the next Monday math club meeting.
ReplyDeleteOk Thank you
ReplyDeleteHello?
ReplyDeleteThis comment has been removed by the author.
ReplyDelete60 cars
ReplyDeleteNidhi, you've gotten the correct answer, but we would like to see your solution.
ReplyDeleteI knew that 78 wasn't divisible by 15 without a remainder, so I tried to see (by subracting 9) what was a number right before 78 where 15 was perfectly divisible by it, and if you added a multiple of 9, you would get 78. I got 60.
ReplyDelete60/4=15
60+9*2=78
Nidhi, you may post your problem now.
ReplyDeleteNidhi, when r u going to post the problem?
ReplyDeleteHello?
ReplyDeleteArt leaves home at 10:00 a.m., driving at 50 miles per hour. At 11:30 a.m., Jennifer leaves home going the same direction, at 45 miles per hour. When will they be 100 miles apart?
ReplyDeleteSorry for the delay guys!
I'm not on the math team, but Mr. Pearson said I could post the answer to some of these questions. Anyway, the answer is 4:30 p.m.
ReplyDeleteAt 50 mph, in 1.5 hrs. Art would be 75 miles away from Jennifer. Every hour he would get 5 more miles away. So, 5 hours after 11:30, Art would be 100 miles away, which is 4:30.
Hello?
ReplyDeletehi
ReplyDeleteTroy, you have got to wait until one of them says your right before you can post your problem.
ReplyDeleteI didn't post my problem. That was my solution.
ReplyDeleteHello?
ReplyDeleteTroy, welcome to the marathon! Great work on solving the problem. Your approach is nice, but there's an algebraic way to do it too:
ReplyDeleteLet's call Art's time t. Then, Jennifer's time becomes (t - 1.5). Since d = s × t, we have the equation:
50t - (t - 1.5) × 45 = 100
Solving, we have t = 6.5
6.5 hours after 10:00 A.M. is 4:30 P.M.
The algebraic way might look a little complicated, but it would always lead you to the correct answer no matter how large the numbers are.
You're entitled to post a problem now.
Also, check the weekly problems and see if you can do some. :-)
Alright. Here's my problem.
ReplyDeleteYour brother, Jack is 2 years less than twice your sister Jen's age. The sum of 2 times Jack's age and 3 times Jen's age is 66. What are their ages?
2je - 2 = jack
ReplyDelete2ja + 3je = 66
substitute
2(2je- 2) + 3je = 66
4je - 4 + 3je =66
7je = 70
je = 10
2(10) - 2 = ja
20 - 2 = ja
ja = 18
jennifer is 10 years old
jack is 18 years old
Wonderful job, Vishal! You may post your problem now.
ReplyDeleteProblem #?
ReplyDeleteMr.and Mrs.Generous invited 3 friends to dinner at a restaurant. The average cost of each person's dinner was 35. There was a 10% service charge and a 2% tax on the dinner. How much did Mr.Generous have to pay altogetherfor the dinner?
Hello? Anyone....
ReplyDeleteWhat should I do?
ReplyDeleteDon't worry about it.... it's fine.
ReplyDeleteANYONE THERE!
ReplyDeleteI'm here...
ReplyDelete$196
ReplyDelete35*5 =$175
10% of 175 =$17.5
2% of 175 =$3.50
Grand Total=$196
Good job, Troy. You can post your problem now. It will be Problem 20. Please mention the problem number when you post.
ReplyDeleteGood Job Troy
ReplyDeleteProblem 20
ReplyDelete5 hockey pucks and 3 hockey sticks cost $23
5 hockey pucks and 1 hockey stick costs $20
How much does each cost?
Hey, Troy. We'd love to have you join math club! Come tomorrow morning at 8:00 to Mr. Pearson's room if you can.
ReplyDeleteYou'll receive competition info and practice stuff there.
5hp + 3hc = 23
ReplyDelete5hp + hc = 20
hc = 20 - 5hp
5hp + 3( 20 -5hp) = 23
5hp + 60 - 15hp = 23
-10 hp = -37
hp = 3.7
5hp + hc = 20
3.7 x 5 +hc = 20
18.5 + hc = 20
hc = 1.5
A hockey puck is $3.7 each
A hockey stick is $ 1.5 each
p.s are we meeting tommorow
hello?
ReplyDeleteWell done.
ReplyDeleteYour substitution method is correct, only it would probably save time if you use elimination.
hockey puck = p
hockey stick = s
5p + 3s = 23 ⇒ Equation 1
5p + s = 20 ⇒ Equation 2
(Equation 1) - (Equation 2) ⇒ 2s = 3 ⇒ s = 1.50
Then, 5p = 20 - 1.50 = 18.50 ⇒ p = 3.70
I'm going to email all the Chapter Round participants to meet on Wednesday morning.
ReplyDeletePlease do not miss the meeting since it's the last one before the Chapter Round on February 26th at GA Tech.
Ok
ReplyDeleteProblem ?
ReplyDeleteThere are 340 children at a park. 2/5 of the boys is equal to 4/7 of the girls. How many girls and how many boys are there at the park?
Have fun guys!
ReplyDeleteHello?
ReplyDeleteHello?
ReplyDeleteHello?????????
ReplyDeleteVishal, it looks like no one is visiting the blog ... so would you like for me to post a few problems for you?
ReplyDeleteSure Agni.
ReplyDeleteHello?
ReplyDelete