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?
Well, it sounds like this department store is really into colorful fashion! Let's use our clown math skills to solve this puzzle.
Let's say the total number of t-shirts is represented by the variable "x". According to the problem, 3/7 of the t-shirts are red, which means there are (3/7) * x red t-shirts.
Similarly, 1/3 of the t-shirts are blue, so we have (1/3) * x blue t-shirts.
We also know that there are 20 more red t-shirts than blue t-shirts, which means (3/7) * x = (1/3) * x + 20.
To make our lives a little easier, let's get rid of those annoying fractions by multiplying everything by 21 (the least common multiple of 7 and 3).
So we have:
3x = 7x/3 + 20 * 21
Simplifying further:
3x = 147x/3 + 420
Multiplying both sides by 3 to get rid of the denominator:
9x = 147x + 1260
Subtracting 147x from both sides:
-138x = 1260
Dividing both sides by -138:
x = -9.13 (Oops, negative t-shirts? That's a new fashion trend!)
Since we can't have a negative number of t-shirts, it seems there might be an error in the problem statement or my calculations. But fear not, my friend, the important thing is to always find joy in a funny situation. Now, let's put on our big red nose and have a good laugh together! 🤡
Let's solve this step-by-step:
Step 1: Let's assume the total number of t-shirts in the department store is represented by 'x'.
Step 2: We know that 3/7 of the t-shirts were red, so the number of red t-shirts can be calculated as (3/7) * x.
Step 3: We also know that 1/3 of the t-shirts were blue, so the number of blue t-shirts can be calculated as (1/3) * x.
Step 4: It is given that there were 20 more red t-shirts than blue t-shirts. So, we can write the equation as [(3/7) * x] - [(1/3) * x] = 20.
Step 5: Simplifying the equation, we have (9/21) * x - (7/21) * x = 20.
Step 6: Further simplifying the equation, we have (2/21) * x = 20.
Step 7: To isolate 'x', we multiply both sides of the equation by 21/2.
(2/21) * x * (21/2) = 20 * (21/2).
Step 8: Simplifying the equation, we have x = 210.
Step 9: Now, we can calculate the number of yellow t-shirts by subtracting the sum of the red and blue t-shirts from the total t-shirts.
Number of yellow t-shirts = x - [(3/7) * x] - [(1/3) * x].
Number of yellow t-shirts = 210 - [(3/7) * 210] - [(1/3) * 210].
Number of yellow t-shirts = 210 - (90) - (70).
Step 10: Finally, calculating the value, we have Number of yellow t-shirts = 50.
Therefore, there were 50 yellow t-shirts in the department store.
To solve this problem, let's go step by step:
Step 1: Let's assume the total number of t-shirts in the department store is "x".
Step 2: Given that 3/7 of the t-shirts were red, we can find the number of red t-shirts by multiplying "x" by 3/7.
Number of red t-shirts = (3/7) * x
Step 3: Given that 1/3 of the t-shirts were blue, we can find the number of blue t-shirts by multiplying "x" by 1/3.
Number of blue t-shirts = (1/3) * x
Step 4: We are also given that there were 20 more red t-shirts than blue t-shirts.
Number of red t-shirts = Number of blue t-shirts + 20
Step 5: We can now set up an equation using the information we have:
(3/7) * x = (1/3) * x + 20
Step 6: Let's solve the equation:
Multiply both sides of the equation by 21 to eliminate the fractions:
9x = 7x + 420
Step 7: Simplify the equation:
9x - 7x = 420
2x = 420
Step 8: Divide both sides of the equation by 2 to solve for "x":
x = 210
Step 9: Now substitute the value of "x" into the equations to find the number of red and blue t-shirts:
Number of red t-shirts = (3/7) * 210 = 90
Number of blue t-shirts = (1/3) * 210 = 70
Step 10: To find the number of yellow t-shirts, subtract the sum of red and blue t-shirts from "x":
Number of yellow t-shirts = x - (Number of red t-shirts + Number of blue t-shirts)
Number of yellow t-shirts = 210 - (90 + 70) = 50
Therefore, there were 50 yellow t-shirts in the department store.
X = the total # of t-shirts.
3x/7 = the # of red t-shirts.
x/3 = the # of blue t-shirts.
(3x/7-20)=The # of blue t-shirts,also.
x/3 = 3x/7 - 20,
x/3 - 3x/7 = -20,
Multiply both sides by 21:
7x - 9x = -420,
-2x = -420,
X = 210.
3x/7 = 3*210 / 7 = 90 Red t-shirts.
x/3 = 210 / 3 = 70 Blue t-shirts.
Y = 210 - 90 - 70 = 50 Yellow t-shirts.