Question

A bike shop offers three kinds of cycles—tricycles, bicycles, and unicycles. Together, the cycles in the shop have a total of 98 wheels and 46 seats. (Tricycles have 3 wheels, bicycles have 2 wheels, and unicycles have 1 wheel. All cycles have 1 seat.) There are twice as many bicycles as tricycles. How many of each type of cycle are in the shop?

Answer 1

There are 13 tricycles, 26 bicycles, and 7 unicycles.

Explanation:

Let t=the number of tricycles, b=the number of bicycles, and u=the number of unicycles.

Equation to find the number of wheels:

3t+2b+u=98

This can be found because we know that each tricycle has 3 wheels, so we multiply the number of tricycles by 3. This can be done with bicycles and unicycles as well.

Equation to find the number of seats:

t+b+u=46

We know that there are two times as many bicycles as there are tricycles, this can be represented by the equation b=2t.

We can plug this into our number to wheels equation to get:

3t+2(2t)+u=98

3t+4t+u=98

7t+u=98

u=-7t+98

We can also put this into out number of seats equation to get:

t+2t+u=46

3t+u=46

u=-3t+46

Set the equations equal to each other to get:

-7t+98=-3t+46

-4t+98=46

-4t=-52

t=13

b=2t

b=2(13)

b=26

b+t+u=46

26+13+u=46

39+u=46

u=7

There are 13 tricycles, 26 bicycles, and 7 unicycles.