sally put red ,white,and blue handkerchiefs in a drawer. One-third of the hand kerchiefs were red ,one -fourth of the hamdkerchiefs were white and ten were blue. how many handkerchiefs of each color were there?
1/3 +1/4 = 4/12 + 3/12 = 7/12
so 5/12 = 10 are blue
blue = 24 , got it ?
To solve this problem, we need to break it down into steps and use the given information to find the number of handkerchiefs of each color. Let's go step by step:
Step 1: Let's assume the total number of handkerchiefs is represented by "x". Therefore, we have:
Total = x
Step 2: According to the problem, one-third of the handkerchiefs were red. So, the number of red handkerchiefs is (1/3) * x.
Red = (1/3) * x
Step 3: Similarly, one-fourth of the handkerchiefs were white. So, the number of white handkerchiefs is (1/4) * x.
White = (1/4) * x
Step 4: It is also mentioned that ten handkerchiefs were blue. Hence, the number of blue handkerchiefs is 10.
Blue = 10
Now, our goal is to find the values of Red, White, and Blue handkerchiefs by finding the value of "x". We can do this by finding a common denominator for 3 and 4 (which is 12) and setting up an equation using the given information.
(1/3)x + (1/4)x + 10 = x
To solve this equation, multiply through by 12 to clear the fractions:
4x + 3x + 120 = 12x
Combine like terms:
7x + 120 = 12x
Subtract 7x from both sides:
120 = 5x
Divide both sides by 5:
x = 24
So, we have found the total number of handkerchiefs (x = 24).
Now, let's substitute this value back into our equations from steps 2 and 3 to find the respective values for Red and White.
Red = (1/3) * 24 = 8
White = (1/4) * 24 = 6
Therefore, there are 8 red handkerchiefs, 6 white handkerchiefs, and 10 blue handkerchiefs in the drawer.