### Brain Teasers

# Tricycles

There are a total of 14 bicycles and tricycles. If the total number of wheels is 34, how many tricycles are there?

### Answer

2(b) + 3(t) = 34[2 * bicycles + 3 * tricycles = amount of wheels]

b + t = 14

[bicycles + tricycles = 14]

Manipulate the second equation to exclude a variable:

b + t - t = 14 - t

b = 14 - t

Then combine the two statements to keep true and solve:

2(14 - t) + 3(t) = 34

28 - 2t + 3t = 34

t = 6

If b = 14 - t

b = 14 - 8

b = 8

Therefore there are 6 tricycles and 8 bicycles.

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## Comments

Have you got a method to show us how you got he answer Michelle or is it just trial and error?

Well, I'm not Michelle, but an easy way is: first think the vehicles are only bicycles. That makes 28 wheels. 6 wheels are left to complete the tricycles (1 wheel to turn a bicycle into a tricycle). I wish you a nice day.

You figure it out like this:

2(b) + 3(t) = 34

[2 * bicycles + 3 * tricycles = amount of wheels]

b + t = 14

[bicycles + tricycles = 14]

Manipulate the second equation to exclue a variable:

b + t - t = 14 - t

b = 14 - t

Then combine the two statements to keep true and solve:

2(14 - t) + 3(t) = 34

28 - 2t + 3t = 34

t = 6

If b = 14 - t

b = 14 - 8

b = 8

Therefore there are 6 tricycles and 8 bicycles.

I think we learned this in Grade 6 didn't we?

2(b) + 3(t) = 34

[2 * bicycles + 3 * tricycles = amount of wheels]

b + t = 14

[bicycles + tricycles = 14]

Manipulate the second equation to exclue a variable:

b + t - t = 14 - t

b = 14 - t

Then combine the two statements to keep true and solve:

2(14 - t) + 3(t) = 34

28 - 2t + 3t = 34

t = 6

If b = 14 - t

b = 14 - 8

b = 8

Therefore there are 6 tricycles and 8 bicycles.

I think we learned this in Grade 6 didn't we?

absolutely right sane. that's why the editors have copied your whole solution in the answer to this teaser

Setting this up as an algebra problem is pointless.

34 - 2 x 14 = 6

If they were all bikes you'd have 28 wheel. For each ttike you gain one wheel, so you need six trikes.

Seriously, using algebra to do a problem like this is like using a shotgun to kill a mosquito: it's overkill. Engage your brain before reflexively resorting to algebra to solve every problem that can be solved by algebra. There are so many other tools available and a little reasoning and logic goes a long way.

34 - 2 x 14 = 6

If they were all bikes you'd have 28 wheel. For each ttike you gain one wheel, so you need six trikes.

Seriously, using algebra to do a problem like this is like using a shotgun to kill a mosquito: it's overkill. Engage your brain before reflexively resorting to algebra to solve every problem that can be solved by algebra. There are so many other tools available and a little reasoning and logic goes a long way.

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