The ratio of mountain bikes to the total number of bikes on display in Kent’s bike shop was 2:7. 2/5 of the remaining bikes on display were road bikes and the rest were kids bikes and trick bikes in the ratio of 10:3. If there were 16 more kids bikes than mountain bikes, how many trick bikes were there?

Answer 1

Suppose each is x
mountain bikes are 2x
total bikes are 7x
remaining bikes are 7 - 2 = 5x
road bikes are 2(5 * 5x = 2x
kids and trick bikes are (5-2)x = 3x
kids bikes are 10/13 * 3x trick bikes are 3/13 * 3x
10/13 * 3x - 2x = 16
(30x-26x)/13 = 16
4x = 13 * 4 * 4
x = 52
3/13 * 3x = 3/13 * 3 * 52 = 36

Answer 2

Assume the total number of bikes is x
Then the total number of mountain bikes is 2/7x
The number of road bikes is 2/5 * 5/7x = 2/7x
The number of kids bikes is 10/13 * (1-2/7-2/7)x = 10/13 * 3/7x = 30/91x
According to the meaning of the question,
30/91x - 2/7x = 16
That is 6/91x = 16
Therefore x = 16 * 91/4 = 364
So there were 364 total bikes.
The number of trick buses is
364 * 3/13 * (1 - 2/7 - 2/7) = 364 * 3/13 * 3/7 = 36
There were 36 trick bikes