Question

The owner of a bicycle shop reported his inventory of bicycles and tricycles in an unusual way. He said he counted 79 wheels and 60 pedals. How many bicycles and how many tricycles did he have?

a) 15 bicycles, 5 tricycles
b) 20 bicycles, 10 tricycles
c) 25 bicycles, 15 tricycles
d) 30 bicycles, 20 tricycles

Answer 1

We set up a system of equations based on the information given. However, we find that there is no solution to the system of equations, so we cannot determine the number of bicycles and tricycles.

Step-by-step explanation:

We can set up a system of equations based on the information given. Let's denote the number of bicycles as x and the number of tricycles as y. Each bicycle has 2 wheels and 2 pedals, while each tricycle has 3 wheels and 3 pedals.

From the given information, we can create the following equations:

• 2x + 3y = 79 (the total number of wheels)
• 2x + 3y = 60 (the total number of pedals)

We can solve this system of equations to find the values of x and y. Multiplying the first equation by 2 and the second equation by -3, we can eliminate the x term:

• 4x + 6y = 158
• -6x - 9y = -180

Adding these two equations together, we get:

• -2x - 3y = -22

Multiplying this equation by -1, we can simplify it to:

• 2x + 3y = 22

So, we have:

• 2x + 3y = 22
• 2x + 3y = 60

Subtracting the first equation from the second equation, we get:

• 60 - 22 = 3y - 3y

This simplifies to:

• 38 = 0

This is a contradiction, which means there is no solution to the system of equations. Therefore, the owner of the bicycle shop made a mistake or there is missing information in the question. We cannot determine the number of bicycles and tricycles based on the given information.