the product of two positive numbers is 9 18/25 and one of them is three times the other. find the numbers.
X = 1st. number, 3X = 2Nd number.
3X*X = 9 18/25
3X^2 = 9 18/25 = 243/25
X^2 = 243/75 = 81/25
X = sqrt(81/25) = 9/5 = 1 4/5 = 1st number
3X = 3 * 9/5 = 27/5 = 5 2/5 = 2Nd
number.
Data:
let x and y are two possative numbers
xy = 9 18/25 = 243/25
x = 3y
calculate
x = ?
y = ?
Solution
xy = 243/25
3y.y = 243/25
3y2 = 243/25
divide 3 to both side
y2 = 81/25
square root to both side
y = 9/5
for x
x = 3y
x = 3.9/5
x = 27/5
hence two positive number are 9/5 and 27/5
To find the two positive numbers, let's represent them as x and y.
According to the given information, the product of the two numbers is 9 18/25, which can be written as a mixed number: 9 + 18/25.
So we have the equation: x * y = 9 18/25.
Now, it is also given that one of the numbers (let's say x) is three times the other (y). We can express this information as: x = 3y.
To solve for the unknowns, we'll substitute the value of x in terms of y into the equation:
(3y) * y = 9 + 18/25
Expanding this equation, we get:
3y^2 = 9 + 18/25
To simplify the right-hand side, we need to convert the mixed number into an improper fraction:
9 + 18/25 = (9 * 25 + 18) / 25 = 243/25
Our equation now becomes:
3y^2 = 243/25
To isolate y, we divide both sides of the equation by 3:
y^2 = (243/25) / 3
y^2 = 243/75
Simplifying the right-hand side:
y^2 = 27/25
Taking the square root of both sides, we get:
y = √(27/25)
Now, y could be either the positive or negative square root of 27/25. However, since we are looking for positive numbers, we take the positive square root.
y = √(27/25) = √27 / √25 = 3√3 / 5
Now that we have the value of y, we can find the value of x by substituting it into the equation x = 3y:
x = 3 * (3√3 / 5) = 9√3 / 5
Therefore, the two positive numbers are x = 9√3 / 5 and y = 3√3 / 5.