I have no clue how to figure this out! Can you tell me how to figure it out?

2 positive numbers are in a ratio of 9 to 10. if the lesser number is decreased by 6 and the greater number is decreased by 25, the resulting ratio is 2 to 1. find the greatest of the original numbers.

the original numbers are 9x and 10x

then (9x-6) : (10x-25) = 2 : 1

(9x-6)/(10x-25) = 2

solve this and sub your value of x into 10x

Sure! To solve this problem, we can start by establishing the ratio between the two positive numbers.

Let's assume the two numbers are x and y. According to the problem, the ratio between x and y is 9:10, which can be written as:

x/y = 9/10

Next, the problem states that if the lesser number (x) is decreased by 6 and the greater number (y) is decreased by 25, the resulting ratio is 2:1. We can now set up a new equation with the adjusted values:

(x - 6)/(y - 25) = 2/1

Now, we have two equations:

x/y = 9/10 (Equation 1)
(x - 6)/(y - 25) = 2/1 (Equation 2)

To find the greatest of the original numbers (y), we will solve this system of equations using the method of substitution or elimination.

Let's solve Equation 1 for x:
x/y = 9/10

Multiply both sides of the equation by y:
x = (9/10) * y

Next, substitute this expression for x in Equation 2:

((9/10) * y - 6)/(y - 25) = 2/1

Now, we have an equation with a single variable (y). We can solve this equation to find the value of y, which represents the greatest of the original numbers.