SOLUTION: Sorry I don't know which type it is. Question: It is given that the ratio of two numbers is 3:7. If 6 is subtracted from both numbers, their ratio will become 1:3. What is the ra

Question 1090120: Sorry I don't know which type it is.
Question:
It is given that the ratio of two numbers is 3:7. If 6 is subtracted from both numbers, their ratio will become 1:3. What is the ratio of number if 6 is added to both numbers?
Thank you very much!
Found 2 solutions by Theo, htmentor:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
x/y = 3/7 -> 7x = 3y -> y = 7/3x
(x-6)/(y-6) = 1/3
Substitute the value for y above in the 2nd equation
(x-6)/((7/3)x-6) = 1/3
Solve for x:
3x - 7/3x = 12
This gives x = 18
Thus y = 7*18/3 = 42
So the ratio if 6 is added to both is 24/48 = 1/2

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