Brain Teasers
Auction Action
Nina and her mom helped organize the auction fundraiser to help pay for the 8th grade musical. Seven local stores each donated a gift certificate to be redeemed for merchandise. The gift certificates will be auctioned off at the big event.
The Athlete's Alley, Bay State Basement, CD Corner, Don's Deli, Elk's Software, Fancy Footwear Shop, and the Gorgeous Candy Boutique have all participated.
The gift certificates are each in multiples of $5. There is a $100 range in the value of the gift certificates, which start at $25. The mean value of all seven gift certificates is $80, and the median and the mode are both $70.
The certificate from The Athlete's Alley is worth the most, and the one from Gorgeous Candy is worth the least.
The total value of the gift certificates from CD Corner, Don's Deli, and the Fancy Footwear Shop is $270, but the Fancy Footwear certificate is worth $50 more than the one from Don's Deli. The CD Corner gift certificate is equivalent to the mean for this group of 3 stores.
What is the value of the gift certificate from each store?
The Athlete's Alley, Bay State Basement, CD Corner, Don's Deli, Elk's Software, Fancy Footwear Shop, and the Gorgeous Candy Boutique have all participated.
The gift certificates are each in multiples of $5. There is a $100 range in the value of the gift certificates, which start at $25. The mean value of all seven gift certificates is $80, and the median and the mode are both $70.
The certificate from The Athlete's Alley is worth the most, and the one from Gorgeous Candy is worth the least.
The total value of the gift certificates from CD Corner, Don's Deli, and the Fancy Footwear Shop is $270, but the Fancy Footwear certificate is worth $50 more than the one from Don's Deli. The CD Corner gift certificate is equivalent to the mean for this group of 3 stores.
What is the value of the gift certificate from each store?
Answer
The Athlete's Alley $125Bay State Basement $70
CD Corner $90
Don's Deli $65
Elk's Software $70
Fancy Footwear Shop $115
Gorgeous Candy Boutique $25
Explanation:
Since the mean of all gift certificates is $80, and there are 7 stores, the total of all gift certificates is $560.
The values of the gift certificates range from $25 to $125, therefore the gift certificate from Athlete's Alley is $125 and the gift certificate from Gorgeous Candy Boutique is $25.
This leaves $410 in gift certificates from the other 5 stores.
The gift certificates from CD Corner, Don's Deli and Fancy Footwear Shop total $270. The mean of this group is $90, which is value of the certificate from the CD shop.
This leaves $180 for Don's Deli and Fancy Footwear. Because Fancy Footwear is worth $50 more, the certificate from Don's Deli is half of $130, or $65 dollars, and the certificate from Fancy Footwear is $115.
This leaves the certificates from Bay State Basement and Elk's Software, totalling $140. There's only way to meet the requirement that the median and mode of the 7 values is $70. Both remaining certificates must be valued at $70.
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Comments
please write comments i need feed back!
Loved it. The combination of basic algebra skills with that learned on the first day of stats 101 made this a fun teaser and a nice review. Looking forward to more like it.
i love math and im good at it so it made that fun and easy
Good teaser!
way to long for my redading compacity
Do you think it's best to have the least possible amount of info made available? For instance, I was going through this problem and had each store matched to a dollar amount, so I was done, and then I read "The CD Corner gift certificate is equivalent to the mean for this group of 3 stores." This was a good check, but I already had the answer and think this info was superfluous.
I found it neat in that all there really was to it was F and D, though it looks alot more complicated at first glance!
this teaser is great. i got the right answers! lol
Great! this one forced me to review median and mode to get the answer, so thank you for getting me to think!!!
Great! this one forced me to review median and mode to get the answer, so thank you for getting me to think!!!
To nousheen:
How do you figure that this clue is "superfluous"?
"The CD Corner gift certificate is equivalent to the mean for this group of 3 stores."
Without that info, we could come to other answers for Don's Deli and Fancy Footwear.
Since the three equal $270 and FF is $50 more than DD, we could come up with this:
FF=110 DD=60 CC=100
The only way to solve this part is to know the value of CC by using the superfluous clue above.
If you ask me, I think the use of the word "superfluous" was a bit superfluous.
How do you figure that this clue is "superfluous"?
"The CD Corner gift certificate is equivalent to the mean for this group of 3 stores."
Without that info, we could come to other answers for Don's Deli and Fancy Footwear.
Since the three equal $270 and FF is $50 more than DD, we could come up with this:
FF=110 DD=60 CC=100
The only way to solve this part is to know the value of CC by using the superfluous clue above.
If you ask me, I think the use of the word "superfluous" was a bit superfluous.
im pretty good at math so it wasnt that hard 4 me...i got it but it took me a lil longer than i expected...i luv it...!
Great job!! I enjoyed it.
None of the clues were superfluous.
Keep up the good work (and go Irish!!)
None of the clues were superfluous.
Keep up the good work (and go Irish!!)
Great teaser! I thought it might be tedious, but it was elegant instead. Nice job!
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