The average of 1/5 and other two numbers out of which one is the half of the other is 1/4. What is the smallest fraction out of unknowns.
(1/5 + 2x + x) / 3 = 1/4
3x = 3/4 - 1/5
Let's denote the unknown numbers as x and y, with y being half of x.
According to the given information, the average of 1/5, x, and y is 1/4.
The average of three numbers is found by adding them up and dividing by 3. So we have the equation:
(1/5 + x + y) / 3 = 1/4
To solve for x and y, we need to simplify the equation by multiplying through by the common denominator, which is 60:
(12 + 60x + 60y) / 3 = 15
Now we can simplify further:
12 + 60x + 60y = 45
Next, we know that y is half of x, so we can substitute y with x/2 in the equation:
12 + 60x + 60(x/2) = 45
Simplifying,
12 + 60x + 30x = 45
Combining like terms,
90x = 33
Dividing both sides by 90,
x = 33/90
Simplifying the fraction,
x = 11/30
Since x is the smaller fraction out of the two unknown numbers, the smallest fraction out of the unknowns is 11/30.
To solve this problem, let's assign variables to the unknown numbers. Let's call one of the unknown numbers "x" and the other "y," where y is half of x.
According to the problem, the average of 1/5 and the two unknown numbers is 1/4.
The average of three numbers is found by adding them together and dividing the sum by 3. So, we can set up the following equation:
[(1/5) + x + y] / 3 = 1/4
Since y is half of x, we can express y in terms of x: y = (1/2)x.
Substituting this value into the equation, we get:
[(1/5) + x + (1/2)x] / 3 = 1/4
Simplifying this equation, we have:
[10(1/5) + 10x + 5x] / 30 = 1/4
(2/5 + 15x) / 30 = 1/4
Cross-multiplying, we get:
(2/5 + 15x) * 4 = 30
8/5 + 60x = 30
Now, let's isolate x by subtracting 8/5 from both sides:
60x = 30 - 8/5
We need to convert 30 to an improper fraction with a denominator of 5 to make it easier to subtract:
30 = 150/5, so the equation becomes:
60x = 150 - 8/5
Now, let's convert 150 to a fraction with a denominator of 5:
150 = 750/5, so the equation becomes:
60x = 750/5 - 8/5
Combining the fractions, we have:
60x = (750 - 8)/5
Simplifying the numerator, we get:
60x = 742/5
To find the value of x, we need to divide both sides of the equation by 60:
x = 742/5 ÷ 60
Simplifying, we have:
x ≈ 12.37
Since y is half of x, we can find the value of y by dividing x by 2:
y ≈ 12.37 / 2
y ≈ 6.19
Now, we have the values of x and y. To find the smallest fraction out of x and y, we compare them.
x ≈ 12.37 and y ≈ 6.19
Since the numerator of y (6.19) is smaller than the numerator of x (12.37), y is the smallest fraction out of the unknowns.
Therefore, the smallest fraction out of the unknowns is approximately 6.19.