SOLUTION: Sumana's age is 2 times greater than the age of her brother. 3 years ago, Sumana's age was 3 times the age of her brother. Find Sumana's age.

Question 1049703: Sumana's age is 2 times greater than the age of her brother.
3 years ago, Sumana's age was 3 times the age of her brother.
Find Sumana's age.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x equal the current age of sumana.

let y equal the current age of her brother.

your first equation becomes x = 2 * y.

this equation says that sumana's age is 2 times the age of her brother.

3 years ago, sumana's age was 3 times the age of her brother.

the equation for this would be:

x - 3 = 3 * (y - 3)

if her age today is x, then her age 3 years ago has to be x - 3.
if his age today is y , then his age 3 years ago has to be y - 3.

you have two equations that need to be solved simultaneously.
this means that the same solution has to apply to both equations.

the equations are:

x = 2 * y
(x-3) = 3 * (y-3)

simplify the second equation as follows:
start with x - 3 = 3 * (y - 3)
simplify to get x - 3 = 3 * y - 9
solve for x to get x = 3 * y - 6

your first equation states that x = 2 * y
your second equation states that x = 3 * y - 6

this means that 2 * y must be equal to 3 * y - 6 because they are both equal to x.

the equation you now need to solve is 2 * y = 3 * y - 6
subtract 2 * y from both sides of this equation and add 6 to both sides of this equation to get 2 * y - 2 * y + 6 = 3 * y - 2 * y - 6 + 6
the 2 * y - 2 * y on the left cancels out and the -6 + 6 on the right cancels out and you are left with 6 = 3 * y - 2 * y
simplify to get 6 = y

that should be your answer.

you have y = 6.

in the first equation of x = 2 * y, replace y with 6 and solve for x to get x = 12.

in the second equation of x - 3 = 3 * (y - 3), replace x with 12 and y with 6 to get 12 -3 = 3 * (6 - 3).
simplify to get 9 = 3 * 3.
simplify further to get 9 = 9, which is true.

this confirms the solution is correct.

sumana's age is 12 and her brother's ages is 6.
she is 2 times as old as her brother because 12 is 2 * 6.

3 years ago, she was 9.
3 years ago, he was 3.
her age 3 years ago is 3 * his age 3 years ago because 9 is 3 * 3.

the solution looks good.

her age is now 12.
his age is now 6.
her age 3 years ago was 9.
his age 3 years ago was 3.

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