Brain Teasers
Bikes
Apple Lake Bike Shop has a total of 32 bicycles and tricycles for rent. The shop owner checked all 74 wheels at the beginning of the season to make sure they were in good condition. None of the bicycles had training wheels.
How many of them are bicycles and how many are tricycles?
How many of them are bicycles and how many are tricycles?
Hint
Can there be 16 tricycles and 16 bicycles? Why not?Answer
By guessing numbers of each kind that add to 32, and calculating the number of wheels they have, you will find that the bike shop has 22 bicycles and 10 tricycles.Hide Hint Show Hint Hide Answer Show Answer
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Comments
Congratulations on your first teaser! But it isn't necessary to guess numbers, you can solve two simple equations: b+t=32 and 2b+3t=74.
or u can just see that 74- 2 times 32 is 10, answer.
wow im a genius!
I was hoping that you'd work it out in algebra so i could find out how to use algebra for that sort of stuff. Oh well, it was still pretty good.
very good
Why are you interested in cycles pp? I thought ponies were your preferred mode of transport?
As for the method, I personally prefer logic over mechnanical type algebraic manipulation.
Assume all 32 cycles are bicycles. That would mean 64 wheels. Since you need ten more wheels, replace 10 of the bicycles with tricycles! Hence 10 and 22.
As for the method, I personally prefer logic over mechnanical type algebraic manipulation.
Assume all 32 cycles are bicycles. That would mean 64 wheels. Since you need ten more wheels, replace 10 of the bicycles with tricycles! Hence 10 and 22.
For Jacintan (looking for algebra)
b + t = 32 (total of both, where b is bikes and t is trikes)
2b + 3t = 74 (total wheels; 2 for bikes and 3 for trikes)
rearranging the first equation we get:
t = 32 - b
substituting that for t in the second equation gives us:
2b + 3*(32 - b) = 74
2b + 96 - 3b = 74 (by multiplying out the 3)
-b + 96 = 74 (combining b terms)
-b = -22 (subtracting 96 from both sides)
b = 22 (multiplying through by -1)
substituting b = 22 into t = 32 - b, we get t = 10.
I prefer the more elgant solution of seeing how many wheels would be missing if they were all bikes, but that's just me...
b + t = 32 (total of both, where b is bikes and t is trikes)
2b + 3t = 74 (total wheels; 2 for bikes and 3 for trikes)
rearranging the first equation we get:
t = 32 - b
substituting that for t in the second equation gives us:
2b + 3*(32 - b) = 74
2b + 96 - 3b = 74 (by multiplying out the 3)
-b + 96 = 74 (combining b terms)
-b = -22 (subtracting 96 from both sides)
b = 22 (multiplying through by -1)
substituting b = 22 into t = 32 - b, we get t = 10.
I prefer the more elgant solution of seeing how many wheels would be missing if they were all bikes, but that's just me...
So easy!!!!!!!!! but fun..........
o that was a really good teaser... but im pretty sure i submitted one that was a lot like it!!
Is that a joke, Pretty Pnyz? This is your teaser.
I'm with Jimbo all the way
These teasers with X feet/wheels/hands/legs and only two values to get there are so trivial by doing them as Jimbo points out.
Yawn. One to two seconds.
Yawn. One to two seconds.
It could also be 16 bicycles and 14 tricycles. 16*2=32 14*3=42 42+32=74
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