Question

88 more bicycles than unicycles, 5 times as many tricycles as unicycles, and 40 more bicycles than tricycles, how many are unicycles

Answer 1

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 \( u \):

- The number of bicycles \( b \) is given by:
\[
b = u + 88
\]

- The number of tricycles \( t \) is given by:
\[
t = 5u
\]

- 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 \( b \):
1. \( b = u + 88 \)
2. \( b = 5u + 40 \)

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:
- The number of bicycles \( b \) is:
\[
b = 12 + 88 = 100
\]

- The number of tricycles \( t \) is:
\[
t = 5 \times 12 = 60
\]

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 \( \boxed{12} \).