# 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?

## 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

## 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

## Let's start by finding the ratio of mountain bikes to the total number of bikes on display. We are given that the ratio is 2:7.

Let's assume the number of mountain bikes is 2x and the total number of bikes is 7x.

Now, let's find the number of road bikes. We are told that 2/5 of the remaining bikes on display were road bikes. The remaining bikes would be (7x - 2x) = 5x.

So, the number of road bikes is (2/5) * 5x = 2x.

Now, let's find the number of kids bikes and trick bikes. We are given that they are in the ratio of 10:3. Let's assume the number of kids bikes is 10y and the number of trick bikes is 3y.

We are also told that there were 16 more kids bikes than mountain bikes. So, 10y - 2x = 16.

Now, we can solve for y by substituting the value of kids bikes in terms of x:

10y - 2x = 16
10(7x/2) - 2x = 16
35x - 2x = 16
33x = 16
x = 16/33

Now, let's substitute the value of x in terms of y to find the number of trick bikes:

3y = 3 * 16/33 = 48/33 = 16/11

So, there are 16/11 trick bikes in Kent's bike shop.

## To find the number of trick bikes, we need to follow a step-by-step approach using the given information.

Let's break down the information we have:

1) The ratio of mountain bikes to the total number of bikes on display is 2:7.

Let's assume the number of mountain bikes is 2x, and the total number of bikes on display is 7x.

2) 2/5 of the remaining bikes on display were road bikes.

Let's calculate the number of road bikes using the information given. The remaining bikes are 7x - 2x = 5x.
So, 2/5 of the remaining bikes are road bikes, which would be (2/5) * 5x = 2x road bikes.

3) The remaining bikes are kids bikes and trick bikes in the ratio of 10:3, and there are 16 more kids bikes than mountain bikes.

Let's calculate the number of kids bikes and trick bikes.
The ratio of kids bikes to trick bikes is 10:3, and there are 16 more kids bikes than mountain bikes.

Let's assume the number of kids bikes is 10y, and the number of trick bikes is 3y.
We also know that the number of kids bikes is 2x (from the previous step) + 16.

Using this information, we can create an equation: 2x + 16 = 10y.

4) Determine the value of x and y.

We can solve the equation from the previous step to determine the values of x and y.

Once we find the values of x and y, we can calculate the number of trick bikes, which is 3y.

Following this step-by-step approach will help us find the number of trick bikes.