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The owner of a bike shop sells unicycles and bicycles and keeps inventory by counting seats and wheels. One day, she counts 20 seats and 28 wheels. The equation representing the total number of seats is [tex]u + b = 20[/tex], where [tex]u[/tex] is the number of unicycles and [tex]b[/tex] is the number of bicycles.

Select the equation representing the number of wheels.

A. [tex]u + 2b = 28[/tex]

B. [tex]u + 2b = 20[/tex]

C. [tex]2u + b = 20[/tex]

D. [tex]2u + b = 28[/tex]

Sagot :

GinnyAnswer
To solve this problem, let's analyze the given information step-by-step and determine the correct equation representing the number of wheels:

1. Understand the Given Information:
- The total number of seats counted is 20.
- This can be represented by the equation [tex]\( u + b = 20 \)[/tex], where [tex]\( u \)[/tex] is the number of unicycles and [tex]\( b \)[/tex] is the number of bicycles.
- The total number of wheels counted is 28.

2. Determine How Each Type of Vehicle Contributes to the Wheel Count:
- A unicycle, by definition, has only 1 wheel.
- A bicycle has 2 wheels.

3. Formulate the Equation Representing the Wheel Count:
- If there are [tex]\( u \)[/tex] unicycles, they contribute [tex]\( u \)[/tex] wheels in total (since each unicycle has 1 wheel).
- If there are [tex]\( b \)[/tex] bicycles, they contribute [tex]\( 2b \)[/tex] wheels in total (since each bicycle has 2 wheels).

4. Combine the Contributions:
- The total number of wheels is the sum of wheels from unicycles and bicycles.
- Therefore, the equation representing the total number of wheels is [tex]\( u + 2b = 28 \)[/tex].

Given these steps and our analysis, the correct equation representing the number of wheels is:

[tex]\[ \boxed{u + 2b = 28} \][/tex]

This corresponds to option:

A. [tex]\(u + 2 b = 28\)[/tex]
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