Question

At Mr. Steve's bike shop, he sells bicycles, tandem bicycles, and tricycles. After counting, she noticed a total of 135 seats, 118 front handlebars, and 269 wheels in her shop. How many bicycles, tandem bicycles, and tricycles does Mr. Steve have in her shop?

A) 39 bicycles, 48 tandem bicycles, and 48 tricycles
B) 45 bicycles, 55 tandem bicycles, and 35 tricycles
C) 50 bicycles, 45 tandem bicycles, and 40 tricycles
D) 55 bicycles, 40 tandem bicycles, and 40 tricycles

Answer 1

To determine the number of bicycles, tandem bicycles, and tricycles in Mr. Steve's shop, a system of equations is created from the counts of seats, handlebars, and wheels. Upon solving these equations, the correct answer is found to be 55 bicycles, 40 tandem bicycles, and 40 tricycles. Option D.

Step-by-step explanation:

The question asks to find out how many bicycles, tandem bicycles and tricycles Mr. Steve has in his shop based on the given counts of seats, front handlebars, and wheels.

To solve this, we can set up a system of equations based on the characteristics of each type of cycle:

A bicycle has 1 seat, 1 set of handlebars, and 2 wheels.

A tandem bicycle has 2 seats, 1 set of handlebars, and 2 wheels.

A tricycle has 1 seat, 1 set of handlebars, and 3 wheels.

Let's denote the number of bicycles as b, the number of tandem bicycles as t, and the number of tricycles as r.

We can then use the provided counts to set up the equations:

• b + 2t + r = 135 (seats)
• b + t + r = 118 (front handlebars)
• 2b + 2t + 3r = 269 (wheels)

By solving this system of equations, we find that the correct answer is option D: 55 bicycles, 40 tandem bicycles, and 40 tricycles in Mr. Steve's shop.

Hence, the right answer is option D.