Kiss those Math Headaches GOODBYE!

Posts tagged ‘Problem of the Week’

Problem of the Week-10/25/2010


Here’s one of those:  “Can you make it?” problems.

Using exactly six toothpicks of equal length, how can you put them together to create four congruent equlateral triangles?

Send your answers as comments to this blog post. You need not worry about incorrect answers being posted. I will post only those answers that are correct, and I will post the first five correct answers on Monday.

Feel free to share this problem with anyone who might like to try it.

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Problem of the Week – 10/18/2010


[Note:  I really am not getting a check from the New Mexico Tourism Department for this post, though I wouldn’t mind if they sent me one!]

Katja and Anthony are on a sightseeing trip in the western United States. Beginning where they land in Santa Fe, NM, they drive 80 miles east to see the historic wild west town of Las Vegas, NM. Then they travel 50 miles north to visit the Kiowa National Grasslands . Next they drive 140 miles west to visit Chaco Canyon National Historical Park. Finally they journey 130 miles south to visit El Malpais National Monument. When they reach El Malpais, how many miles are they from their starting point in Santa Fe?

Please explain how you found your answer, and send answers either as comments to this post, or as emails w/ subject POTW, sent to josh@SingingTurtle.com    I will not post your comments unless and until I determine that it is correct. And then, only on the day when I send out the answer on my blog.

 

Chaco's smaller kivas numbered around 100, eac...

Kivas in Chaco Canyon, New Mexico

 

Problem of the Week — Answer


Answer to the 10/1/2010 Problem of the Week

The problem:  Certain digits appear the same when reflected across horizontal lines or vertical lines. This week’s problem:  which two-digit numerals appear the same when reflected across a horizontal line? Which two-digit numerals appear the same when reflected across a vertical line? To answer, provide the list for the horizontal line and the list for the vertical line.

Solution, sent in by Jo Ehrlein, of Oklahoma City, OK:

Assuming you write the #1 with no serifs, then here are the single digits that are the same when reflected across a horizontal line:1, 3, 8, 0.  That means that the 2 digit numbers that are the same when reflected across a horizontal line are:  10, 11, 13, 18, 30, 31, 33, 38, 80, 81, 83, 88

2 digit numbers are only the same when reflected across a vertical line if both digits are the same AND the individual digits are the same when reflected across a vertical line. The single digits that meet that criteria are1, 8, 000 isn’t a valid 2 digit number.That means the 2 digit numbers that are the same when reflected across a vertical axis are 11 and 88.

Well done, Jo!

So the winner’s circle this week has one member:

Jo Ehrlein, Oklahoma City, OK

And, in Jo’s honor, here is our ceremonial picture of Oklahoma City, home of Ralph Ellison,author of Invisible Man,  if I recall correctly.

 

Oklahoma City

Oklahoma City, OK

 
Congratulations to everyone who worked on this problem. I had some detailed answers that were partially correct.

FYI:  Starting this coming week, I’m going to post the Problem of the Week on Monday for teachers who want to use it early in the week. Answers will be posted mid-week.

Problem of the Week – Answer


Answer to the 9/24/2010 Problem of the Week

The problem —

At Gamesville High, students love their clubs. While 20% of the children in the Hex Club are also members of the Backgammon Club, 80% of children in the Backgammon Club are also members of the Hex Club. The Backgammon Club has 35 children. The question:  how many children are in the Hex Club?

Solution:  Here is the solution, provided by the only person who got it right (name below).

20%=0.2, 80%= 0.8.
Let X = the number of students in the Hex Club
Let Y = the number of students in the Backgammon Club
So:
0.2X=0.8 Y because the 20% and 80% are the same children, the same number of people. It just looks different because the percentages show a relationship between the total numbers in each club.

Speaking of total numbers, the problem tells us how many are in the Backgammon Club: 35. So:
Y=35

We now have two equations. We can substitute the value of Y from the second for the Y in the first and solve for X.
0.2X=0.8 (35)
0.2X=28
X=140
There are 140 students in the Hex Club

Sharron Herring

Sharron has answered my problems many times in the past. So thanks for sharing that solution, Sharon.

Next problem will be posted this Friday, Oct. 1.

Answer to Problem of the Week


Answer to the 9/17/2010 Problem of the Week

Flying Flora is traveling an average speed of 76.4 miles per hour, rounded to the nearest tenth of a mile per hour.

Solution:

Let d = distance between Santa Fe and Las Cruces. So 2d = the distance for the round trip. To get the average speed for a trip with two or more “legs,” add up the distances to get total distance, then divide total distance by total time.

For this trip, we get the time for each “leg” by dividing the distance for the leg by the rate for the leg, using the formula, t = d/r. Traveling from Santa Fe to Las Cruces, Flying Flora’s time was d/105; traveling from Las Cruces to Santa Fe, her time was d/60. So the complete formula for average speed is given by:  (2d) ÷ [(d/105) + (d/60)].  Solving this, the d-terms cancel out, and we are find that the expression simplifies to 76.3, with units of miles per hour. So the answer is
76.4 mph.

The people who got this right —

Chris Mark
Irving Lubliner
Jeanine Rose
Sarah Gopher-Stevens

Congratulations to everyone who worked on the problem.

For anyone seeing this for the first time, the problem is this:

Flying Flora, late as usual for her business meeting, speeds from Santa Fe to Las Cruces at 105 mph. After arriving in Las Cruces, she gets an email alerting her that she was caught by a radar gun and received a speeding ticket (she knows the local DA; otherwise she would have been thrown in jail!). Much chastened, Flora drives back from Las Cruces to Santa Fe at just 60 mph. Your task:  Without using a specific value for the distance between the towns, find Flying Flora’s average rate for the round trip. Please show your work and round off your answer to the nearest tenth of a mile per hour.

Facade of the Cathedral of St. Francis in Sant...

St. Francis Cathedral, Santa Fe, Image via Wikipedia