Question 1090120
the ratio of 2 numbers is 3:7 which can be shown as 3/7.


let x be the first number and y be the second number.


you get x/y = 3/7


if 6 is subtracted from both numbers, their ration becomes 1/3.


you get (x-6)/(y-6) = 1/3


solve for x in each of these equations.


start with x/y = 3/7
multiply both sides by y to get x = 3/7 * y


start with (x-6)/(y-6) = 1/3
multiply by (y-6) to get x-6 = 1/3 * (y-6)
add 6 to both sides to get x = 1/3 * (y-6) + 6


since both expressions are equal to x, you can set them equal to each other to get:


3/7 * y = 1/3 * (y-6) + 6


simplify the expression on the right to get:


3/7 * y = 1/3 * y - 6/3 + 6


multiply both sides of this equation by 21 to get:


21 * 3/7 * y = 21 * 1/3 * y - 21 * 6/3 + 21 * 6


simplify to get:


9 * y = 7 * y - 42 + 126


subtract 7 * y from both sides of and combine like terms to get:


2 * y = 84


solve for y to get y = 42.


when y = 42, the equation of x = 3/7 * y becomes x = 3/7 * 42 which becomes x = 18.


you have x = 18 and y = 42.


therefore x/y = 18/42 which simplifies to 3/7.


likewise (18-6) / (42-6) becomes 12/36 which simplifies to 1/3.


likewise (18+6) / (42+6) becomes 24/48 which simplifies to 1/2.


looks like the solution is good.


the solution is x = 18 and y = 42.


i'm sorry.


that's not the solution.


it's an intermediate result.


the problem asks for the ratio if 6 is added to both numbers.


that solution is 1/2.