Auction ActionMath brain teasers require computations to solve.
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?
AnswerThe Athlete's Alley $125
Bay State Basement $70
CD Corner $90
Don's Deli $65
Elk's Software $70
Fancy Footwear Shop $115
Gorgeous Candy Boutique $25
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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