NumbersThe product of two positive numbers is 11520 and their quotient is 9/5. Find the difference of two numbers.Options64607470

To find the difference between two numbers, we need to first determine what those numbers are.

Let's assume the two numbers are x and y.

We are given two pieces of information:

1. The product of the two numbers is 11520, which can be written as x * y = 11520.
2. The quotient of the two numbers is 9/5, which can be written as x / y = 9/5.

To solve this problem, we can use a system of equations.

From the first equation, we can express one variable in terms of the other. Let's solve for x: x = 11520 / y.

Now we can substitute this expression for x into the second equation: (11520 / y) / y = 9/5.

To simplify this equation, we can multiply both sides by y: 11520 / y = 9/5 * y.

Next, we can cross-multiply to get rid of the fractions: 11520 * 5 = 9 * y^2.

Simplifying further, we have: 57600 = 9 * y^2.

Dividing both sides by 9, we get: y^2 = 6400.

Taking the square root of both sides, we find: y = ±80.

Since we are looking for positive numbers, we can discard the negative solution. Therefore, y = 80.

Now we can substitute this value of y back into the expression for x: x = 11520 / 80 = 144.

The two numbers are x = 144 and y = 80.

To find the difference between these two numbers, we subtract them: 144 - 80 = 64.

Therefore, the difference between the two numbers is 64.