The product of two positive number is5/6 and their quotient is 15/8 . calculate the numbers.
xy = 5/6
x/y = 15/8
6xy = 5
8x/15 = y
6x(8x/15) = 5
48x^2 = 75
x^2 = 75/48 = 25/16
x = 5/4
y = 2/3
Well, it seems like those numbers really like to play hide-and-seek with each other. Let's call the first number x and the second number y. According to the given information, we have two equations:
xy = 5/6
x/y = 15/8
Now, let's solve this puzzle. Let's find the value of x:
xy = 5/6
x = (5/6) / y
Now let's substitute this value of x in the second equation:
(5/6) / y / y = 15/8
Hmm, math seems to be trickier than a clown's tricks here. Let me simplify this equation for you:
[5 / (6y)] / y = 15/8
5 / (6y * y) = 15/8
To make things easier, let's cross-multiply:
40y = 15 * 6y * y
Simplifying further:
40y = 90y^2
Oops, there seems to be something fishy going on here. I'm afraid I can't solve this equation for you, as it doesn't seem to have a solution. Please double-check your values and equations!
Let's denote the two positive numbers as "x" and "y". According to the given information, we have two equations:
1) x * y = 5/6
2) x / y = 15/8
To solve this system of equations, we can use the method of substitution.
First, solve equation 2) for x in terms of y by multiplying both sides by y:
x = (15/8) * y
Substitute this value of x into equation 1):
(15/8) * y * y = 5/6
Simplify the equation:
15y^2 / 8 = 5 / 6
Multiply both sides by the reciprocal of (15/8), which is (8/15):
y^2 = (5/6) * (8/15) = 40/90 = 4/9
Take the square root of both sides to solve for y:
y = sqrt(4/9), or y = 2/3
Substitute this value of y back into the equation we found earlier:
x = (15/8) * (2/3) = 30/24 = 5/4
Therefore, the two positive numbers are x = 5/4 and y = 2/3.
To find the two numbers, let's assume the first number is x and the second number is y.
According to the given information, we have two equations:
Equation 1: x * y = 5/6
Equation 2: x / y = 15/8
We can solve these equations simultaneously to find the values of x and y.
Equation 2 can be rearranged as x = (15/8) * y.
Substituting this value of x into Equation 1:
(15/8) * y * y = 5/6
Multiplying both sides of the equation by 6 to eliminate the fraction:
15 * y * y = 4 * 5
Simplifying:
15y^2 = 20
Dividing both sides of the equation by 15:
y^2 = 20/15
Taking the square root of both sides:
y = ± √(20/15)
Now, we need to determine the positive value for y, so
y = √(20/15)
Next, substitute this value of y back into Equation 2 to find the value of x:
x = (15/8) * √(20/15)
Calculating the expression:
x = (15/8) * (√20 / √15)
Simplifying, we get:
x = 15√5 / (8√3)
Hence, the two numbers are x = 15√5 / (8√3) and y = √(20/15).