In a department store there were a certain number of red tshirts, blue tshirts, and yellow tshirts. 3/7 of the tshirts were red, 1/3 of them were blue, and the rest were yellow. If there were 20 more red tshirts than bake tshirts, how many yellow tshirts were there?

If there were x shirts,

r = 3/7 x
b = 1/3 x
r = b + 20

3/7 x = 1/3 x + 20
x = 210

So, now figure the red and "bake", and the rest are yellow.

Let's start by setting up the given information:

Let the total number of t-shirts be represented as 'x'.
So, the number of red t-shirts is 3/7 * x.
The number of blue t-shirts is 1/3 * x.

We are also given that there were 20 more red t-shirts than blue t-shirts. Let's represent the number of blue t-shirts as 'b'.
So, the number of red t-shirts is 'b + 20'.

Since the remaining t-shirts are yellow, we can set up the equation:
x = (3/7)x + (1/3)x + b + b + 20

Simplifying the equation:
x = (3/7)x + (2/3)x + 2b + 20

Multiplying through by the least common denominator (LCD) of 7 and 3, which is 21:
21x = 9x + 14x + 42b + 420

Combining like terms:
21x = 23x + 42b + 420

Moving all the variables to one side:
0 = 2x - 42b + 420

Now, we can use the information that 'x' represents the total number of t-shirts. Since there cannot be a fraction or decimal for the number of t-shirts, we can set 'x' to be a multiple of 7. Let's assume x = 7.

Substituting x = 7 in the equation:
0 = 2(7) - 42b + 420

Simplifying:
0 = 14 - 42b + 420

Combining like terms:
0 = -42b + 434

Moving the constant term to the other side:
42b = 434

Dividing by 42:
b = 434/42
b = 10.33

We cannot have a fractional value for the number of blue t-shirts. Therefore, there is no solution with the given information.

To find the number of yellow t-shirts, we first need to determine the number of red and blue t-shirts.

Let's denote the number of red t-shirts as "R", the number of blue t-shirts as "B", and the number of yellow t-shirts as "Y".

According to the information given:
- 3/7 of the t-shirts were red, so we have (3/7)(R + B + Y) = R.
- 1/3 of the t-shirts were blue, so we have (1/3)(R + B + Y) = B.
- The rest of the t-shirts were yellow, implying Y = (R + B + Y) - (R + B).

Next, we are told that there were 20 more red t-shirts than blue t-shirts, so R = B + 20.

Substituting this value of R in the first two equations, we have:
(3/7)(B + 20 + B + Y) = B,
(1/3)(B + 20 + B + Y) = B.

Simplifying these equations, we get:
(3/7)(2B + Y + 20) = B,
(1/3)(2B + Y + 20) = B.

Now, we can solve these equations to find the values of B and Y.

To do this, we can use algebraic manipulation.

First, multiply both sides of the equation by 7 to eliminate the denominator:
3(2B + Y + 20) = 7B.

Next, distribute:
6B + 3Y + 60 = 7B.

Combine the like terms:
3Y + 60 = B.

Similarly, multiply both sides of the second equation by 3:
2B + Y + 20 = 3B.

Combine like terms:
Y + 20 = B.

Now, we have two equations:
3Y + 60 = B,
Y + 20 = B.

If we substitute the second equation into the first, we have:
3Y + 60 = Y + 20.

By solving this equation, we can determine the value of Y, which represents the number of yellow t-shirts in the department store.