Let's determine the correct equation representing the number of wheels in this problem.
Given:
- The bike shop owner counts 15 seats.
- The bike shop owner counts 22 wheels.
- Unicycles (u) have 1 wheel each.
- Bicycles (b) have 2 wheels each.
We can write the equations based on the given information:
1. The equation for the total number of seats is:
[tex]\[ u + b = 15 \][/tex]
This equation represents the sum of the seats provided by unicycles and bicycles.
2. The equation for the total number of wheels should account for the wheels of unicycles and bicycles. Since each unicycle has 1 wheel and each bicycle has 2 wheels, the number of wheels can be expressed as:
[tex]\[ 1 \cdot u + 2 \cdot b = 22 \][/tex]
Simplifying this, we get:
[tex]\[ u + 2b = 22 \][/tex]
Thus, the equation representing the number of wheels is:
[tex]\[ u + 2b = 22 \][/tex]
Among the given choices:
A. [tex]\( 2u + b = 22 \)[/tex]
B. [tex]\( u + 2b = 15 \)[/tex]
C. [tex]\( 2u + b = 15 \)[/tex]
D. [tex]\( u + 2b = 22 \)[/tex]
The correct choice should be [tex]\[ u + 2b = 22 \][/tex].
Hence, the correct choice is:
[tex]\[ \boxed{D} \][/tex]
