in a department sore there are red t-shirts, blue t-shirts, and yellow t-shirts. 3/7 of the shirts are red, 1/3 are blue and the rest are yellow. if there were 20 more red than blue, how many were yellow?

let the total t-shirts be x

then,
RED:3x/7

BlUES:x/3

Yellow: x-(3x/7 +x/3)=5x/21

we know reds are 20 more than blues
therefore, 3x/7 =(x/3 +20)
then solve for x by subtracting x/3 both sides
(3x/7)-(x/3)=20
(2x/21)=20 ,multiply 21 both sides to eliminate the denominator ,then you will get,

2x=420

x=210(total t-shirts sold in the store)

we know the yellows are 5x/21
substitute x in 210.
therefore,yellows are (5.210)/21
Yellow= 50

To find the number of yellow t-shirts, let's break down the information given step by step:

1. We know that 3/7 of the t-shirts are red. This means that the red t-shirts represent 3/7 of the total number of t-shirts.
2. We also know that 1/3 of the t-shirts are blue. This means that the blue t-shirts represent 1/3 of the total number of t-shirts.
3. Additionally, it is mentioned that there are 20 more red t-shirts than blue t-shirts.

Now, let's solve for the number of yellow t-shirts:

Let's assume that the total number of t-shirts is represented by "x".

1. The number of red t-shirts is (3/7) * x.
2. The number of blue t-shirts is (1/3) * x.
3. According to the information given, the number of red t-shirts is 20 more than the number of blue t-shirts: (3/7) * x = (1/3) * x + 20.

To solve this equation, we can multiply both sides by the least common denominator (LCD) of 7 and 3, which is 21:

21 * (3/7) * x = 21 * (1/3) * x + 21 * 20.

This simplifies to:

9x = 7x + 420.

Simplifying further, we subtract 7x from both sides:

9x - 7x = 420.

2x = 420.

Finally, dividing both sides by 2:

x = 210.

Now that we know that the total number of t-shirts is 210, we can calculate the number of yellow t-shirts:

The number of yellow t-shirts is the remaining number of t-shirts after accounting for the red and blue t-shirts:

Number of yellow t-shirts = Total number of t-shirts - Number of red t-shirts - Number of blue t-shirts.

Number of yellow t-shirts = 210 - (3/7) * 210 - (1/3) * 210.

Calculating this, we get:

Number of yellow t-shirts = 210 - (3/7) * 210 - (1/3) * 210 = 90.

Therefore, there are 90 yellow t-shirts.