Let's define the number of unicycles as \( u \).
According to the problem, we can express the number of bicycles and tricycles in terms of \( u \):
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The number of bicycles \( b \) is given by: \[ b = u + 88 \]
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The number of tricycles \( t \) is given by: \[ t = 5u \]
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We also know that the number of bicycles is 40 more than the number of tricycles: \[ b = t + 40 \]
Now we can substitute the expressions for \( b \) and \( t \) into the equation \( b = t + 40 \):
Substituting \( t = 5u \) into the equation gives: \[ b = 5u + 40 \]
Now we have two expressions for \( b \):
- \( b = u + 88 \)
- \( b = 5u + 40 \)
We can set these equal to each other: \[ u + 88 = 5u + 40 \]
Now, we can solve for \( u \): \[ 88 - 40 = 5u - u \] \[ 48 = 4u \] \[ u = 12 \]
So, the number of unicycles is \( \boxed{12} \).
Verification
Let's verify the solution:
- If \( u = 12 \), then:
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The number of bicycles \( b \) is: \[ b = 12 + 88 = 100 \]
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The number of tricycles \( t \) is: \[ t = 5 \times 12 = 60 \]
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Now we check if the relationship holds:
- According to the problem:
- Bicycles = Tricycles + 40
- \( 100 = 60 + 40 \) is true.
Thus, the solution is verified, and the number of unicycles is indeed \( \boxed{12} \).