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.