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Kidstuff
Bicycles, tricycles, pedal cars galore
Some have 2 wheels, some 3, some 4
One each they belong to some girls and boys
Eighteen is the number of these toys
If I change 1 tyre a week I fear
To change them all will take me a year
There are half as many cars as trikes
How many of each are owned by these tykes?
Some have 2 wheels, some 3, some 4
One each they belong to some girls and boys
Eighteen is the number of these toys
If I change 1 tyre a week I fear
To change them all will take me a year
There are half as many cars as trikes
How many of each are owned by these tykes?
Hint
How many weeks are there in a year?Answer
Suppose there is 1 car. There are 2 tricycles and 15 bikes. This makes 40 wheels - not enough.Suppose there are 2 cars. There are 4 tricycles and 12 bikes. This makes 44 wheels.
Each time I add 1 car I get 4 extra wheels. I need 52 wheels so I want 2 more cars.
Answer 4 cars, 8 tricycles and 6 bikes.
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Or, to actually solve it, use B+T+C=18 and 2C=T and (knowing 52 weeks/year) 2B+3T+4C=52, substitute 2C for T in B+T+C=18 to get B+2C+C=18 or B=18-3C. Now substitute both T and B out of the other equation to get 2(18-3C)+3(2C)+4C=52 and solve.
I agree with Jim, the hit-and-miss approach is definitely not a shortcut.
This is definitely not a hit and miss approach. It is pattern searching for pre- algebra kids. Any problem of this type can be solved efficiently in 3 steps every time by observing the differences created between values of say 1 and 2 for 1 variable (0 and 1 even easier in some circumstances). Any 12 year old could follow this logic easily but not many can master simultaneous equations in 3 variables!
I solved it as well using the b+t+c formula, though i solved the 52 week formula first and then entered it into the other formula. Although I do show that the other way works, I agree that it is less plausible for many cases where the total of b+t+c would be a higher number than 18 as starting at one and going up would take much longer. Also, my 11 year old has no problem solving multiple equations with 3 variables, but we homeschool, which might be the reason.
I dont get it.
I also got the answer by using the 3 equations. I cant follow the logic presented in the original solution.
I solved it by observing that there were two fewer wheels than an average of three wheels. This meant that there had to be two more bikes than cars with the rest being trikes. Given that there are two trikes for each bike making three equal parts, I just subtracted the two extra bikes from the 18 to make four equal parts and divided 16 in half to get the number of trikes (2 parts) and then divided the remaining 8 in half for cars and trikes.
Sounds long, but the whole thing took about four seconds.
Sounds long, but the whole thing took about four seconds.
Meant to say "two trikes for each car..."
Wow, must have typed the first comment in about four seconds...the last statement should say "divided the remaining 8 in half for cars and bikes."
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