Question

Three months later some vehicles were sold and new models have been brought into the Liberty Bike Shop. Now, there are a different number of bicycles, tandem bicycles, and tricycles in the shop. There are a total of 135 seats, 118 front handlebars (that steer the bike), and 269 wheels.

Answer 1

There 68 bicycles , 33 tricycles and 17 Tandem bicycles

Explanation:

Let B be the no. bicycles , TB be the no. of tandem bicycles and C be the no. of tricycles

No. of seats in 1 bicycle = 1

No. of seats in B bicycle = B

No. of seats in 1 Tandem bicycle = 2

No. of seats in TB Tandem bicycle = 2TB

No. of seats in 1 Tricycle = 1

No. of seats in C Tricycle = C

We are given that There are a total of 135 seats

So, B+2TB+C=135 ----1

Similarly

There are total 118 front handlers

So,1B + 1TB + 1C = 118 ----2

There are total 269 wheels

So,2B + 2TB + 3TR = 269

Substract 1 from 2

B+2TB+C-B-TB-C=135-118

TB=17

Adding 1 and 2 and substracting from 3

[2 - (1+1)]B + [2- (2+1)]TB + [3- (1+1)]C = 269-253

- 1x17 +C= 16

C= 16 + 17 = 33

Replacing in eq. 32

1B + 17 + 33 = 118

B = 118 - 17 - 33 = 68

Hence There 68 bicycles , 33 tricycles and 17 Tandem bicycles