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

Question

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

with no variables like x

Answer 1

There were X t-shirts.

Red = 3x/7.
Blue = x/3.
Yel. = x - (3x/7 + x/3) = x - (9x/21+7x/21) = x - 16x/21 = 5x/21.

R = B + 20.
3x/7 = x/3 + 20.
9x/21 - 7x/21 = 20,
2x/21 = 20,
X = 210 t-shirts.

Yel. = 5x/21 = (5*210)/21 = 50.

Answer 2

Let's solve the problem step-by-step:

Step 1: Determine the fraction of each type of t-shirt:
- The fraction of red t-shirts is 3/7.
- The fraction of blue t-shirts is 1/3.

Step 2: Find a common denominator for 7 and 3, which is 21.

Step 3: Convert the fractions to have a denominator of 21:
- The fraction of red t-shirts is now (3/7) * (3/3) = 9/21.
- The fraction of blue t-shirts is now (1/3) * (7/7) = 7/21.

Step 4: Determine the difference in the number of red and blue t-shirts:
- Given that there were 20 more red t-shirts than blue t-shirts, we can set up the equation: 9/21 - 7/21 = 20.

Step 5: Simplify the equation: 2/21 = 20.

Step 6: Multiply both sides of the equation by 21 to isolate the variable: 2 = 420.

Step 7: Divide both sides of the equation by 2 to solve for the variable: 1 = 210.

Step 8: Determine the number of yellow t-shirts:
- Since the sum of red, blue, and yellow t-shirts is equal to 1, we subtract the fractions of red and blue t-shirts from 1 to find the fraction of yellow t-shirts: 1 - (9/21 + 7/21) = 1 - 16/21 = 5/21.

Step 9: The number of yellow t-shirts can be determined by multiplying 5/21 by the total number of t-shirts. However, since the problem doesn't provide the total number of t-shirts, we cannot determine the specific number of yellow t-shirts without additional information.

Therefore, without the total number of t-shirts given in the problem statement, it is not possible to determine the exact number of yellow t-shirts.

Answer 3

To solve this problem without using variables, we can use a step-by-step approach:

Step 1: Find the total number of t-shirts
We know that 3/7 of the t-shirts were red, 1/3 of them were blue, and the rest were yellow. The sum of these fractions will give us the total number of t-shirts. Since the total number is not given in the question, we can assign it a variable, let's say "T."

3/7(T) denotes the number of red t-shirts and 1/3(T) denotes the number of blue t-shirts.

Step 2: Establish the relationship between the number of red and blue t-shirts
The question states that there were 20 more red t-shirts than blue t-shirts. So we can set up the equation:

3/7(T) = 1/3(T) + 20

Step 3: Solve the equation
We can start by multiplying both sides of the equation by 21 (the least common denominator of 7 and 3) to eliminate the fractions:

3 * 3(T) = 7 * 1(T) + 420

9(T) = 7(T) + 420

2(T) = 420

T = 420/2

T = 210

Step 4: Calculate the number of yellow t-shirts
Since we know the total number of t-shirts is 210, and the red t-shirts account for 3/7 of the total, the number of red t-shirts is:

3/7 * 210 = 90

Similarly, the number of blue t-shirts is:

1/3 * 210 = 70

To find the number of yellow t-shirts, we can subtract the sum of red and blue t-shirts from the total:

210 - 90 - 70 = 50

So, there are 50 yellow t-shirts in the department store.