Brain Teasers
Frank's Fast Food Eatery
FRANK'S FAST FOOD EATERY
Hamburger with toppings $2.25
Fries $0.95
Cola $0.50
Coffee $0.75
Frank's Fast Food Eatery offers a Saturday Soccer Team Special. When student sports teams come in wearing their uniforms and accompanied by their coaches, they can get 1 hamburger free for every 5 they purchase.
The entire Meadowland team wore their uniforms and went to Frank's Eatery for lunch with their 2 coaches. Each person, including the players and coaches, had 1 hamburger with toppings. Each player had a cola and shared a bag of fries with 1 other teammate. The 2 coaches each had his own order of fries and a coffee. The total bill (no tax) for the students and coaches came to $42.10.
How many players are on the team?
Hamburger with toppings $2.25
Fries $0.95
Cola $0.50
Coffee $0.75
Frank's Fast Food Eatery offers a Saturday Soccer Team Special. When student sports teams come in wearing their uniforms and accompanied by their coaches, they can get 1 hamburger free for every 5 they purchase.
The entire Meadowland team wore their uniforms and went to Frank's Eatery for lunch with their 2 coaches. Each person, including the players and coaches, had 1 hamburger with toppings. Each player had a cola and shared a bag of fries with 1 other teammate. The 2 coaches each had his own order of fries and a coffee. The total bill (no tax) for the students and coaches came to $42.10.
How many players are on the team?
Hint
Using the prices on the menu, estimate the possible number of players on the team.Make a chart, work backwards, and then guess and check.
Answer
There were 12 players on the team.Items: Cost
10 Hamburgers (part of special): $22.50
2 Free hamburgers: $0.00
2 Additional hamburgers: $4.50
6 Fries for players: $5.70
2 Fries for coaches: $1.90
12 Colas: $6.00
2 Coffees: $1.50
TOTAL BILL: $42.10
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Comments
I'm not the best at math so it kind of took me a little bit but I eventually got the answer... good teaser
I got close by writing out the equation, then went back and checked. Equations:
If N= number of players
then 0.5N+0.95(N/2)= cost of drinks and fries
AND
3.4= cost of coaches drinks and fries
AND
(2.25*5/6)*(N+2) ~ cost per hamburger
(not actually equal since you only get this if final number is divisible by 6)
So:
41.2 = 3.4 + 0.5N +0.95 (N/2) + (2.25*5/6)*(N+2)
Solve for N gets 12 and change. Therefore I tried 12, using the prices (2.25 per burger *12, since 2 are free) and it works.
Did anyone else have a formula that works directly-- I'm sure there is one, I was just too lazy to figure it out....
Thanks for the fun teaser!!!
If N= number of players
then 0.5N+0.95(N/2)= cost of drinks and fries
AND
3.4= cost of coaches drinks and fries
AND
(2.25*5/6)*(N+2) ~ cost per hamburger
(not actually equal since you only get this if final number is divisible by 6)
So:
41.2 = 3.4 + 0.5N +0.95 (N/2) + (2.25*5/6)*(N+2)
Solve for N gets 12 and change. Therefore I tried 12, using the prices (2.25 per burger *12, since 2 are free) and it works.
Did anyone else have a formula that works directly-- I'm sure there is one, I was just too lazy to figure it out....
Thanks for the fun teaser!!!
scihead that was confusing i guessed 10 but good one!!1
Coming up with the answer didn't take long. Deciding that the problem -- or my approach to solving it -- was not somehow flawed took somewhat longer. In response to another's comment: In order to create a simple equation, I removed the cost of the coaches' coffee and fries. This gives you 38.70. You then have T(2.25 + .50 + 1/2(.95)) = 38.70. Division gives you a nice whole number of 12. If you question the method and result, as I did, you can then go back and check your work by acting as if you were the cashier and totaling the bill for the 12 players and 2 coaches. Then, just subtract the 2 free burgers. Oh, by the way: good work on the part of the teaser creator. Enjoyed it.
I've decided my method for solving this problem (mentioned in the above comment) is flawed. It does not seem to work when I change the number of coaches. I had a feeling it wouldn't. My skills are a bit rusty. This teaser, which initially took about a minute to solve -- likely by mere chance -- has now become the problem on which I have spent more time than any other at this site. I like it.
I too came up with twelve, from an inexact result of an equation equivalent to scihead's above. I don't think there is an exact formula to be composed, as the number of freebies is not a direct function of the number of people. (i.e., any total of people between 12 and 16 would receive 2 free burgers) Good teaser!
the question requires too much of trial and error
I got the answer directly without any trial and error.
First, subtract the two coaches:
42.10 - 2(2.25+.95+.75) = 34.20
Now each pair of players costs:
2(2.25+.50) + .95 = 6.45
After the first four players, you get a free burger, so there's
34.20 - 2*6.45 + 2.25 = 23.55
left after the first four players.
Each additional group of six players costs
3*6.45 - 2.25 = 17.10
Dividing 23.55 by 17.10 gives one group of six players and leaves
23.55 - 17.10 = 6.45
which is just enough for two more players.
4 + 6 + 2 = 12 players
First, subtract the two coaches:
42.10 - 2(2.25+.95+.75) = 34.20
Now each pair of players costs:
2(2.25+.50) + .95 = 6.45
After the first four players, you get a free burger, so there's
34.20 - 2*6.45 + 2.25 = 23.55
left after the first four players.
Each additional group of six players costs
3*6.45 - 2.25 = 17.10
Dividing 23.55 by 17.10 gives one group of six players and leaves
23.55 - 17.10 = 6.45
which is just enough for two more players.
4 + 6 + 2 = 12 players
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