Question 973010: Hi,
I have been trying to solve a word problem, here it is:
Three years ago, Evan was one third of his sister's age. In a year's time, Evan's age doubled will match his sister's age. How old is Evan now?
I know that I need to turn the problem into an equation and then solve, but I can not figure out how to turn the problem into an equation
Thanks
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your problem states:
Three years ago, Evan was one third of his sister's age. In a year's time, Evan's age doubled will match his sister's age. How old is Evan now?
let x = evan's age now.
let y = his sister's age now.
3 years ago, evan was one third of his sister's age.
if x is evan's age now, then evan's age 3 years ago has to be x-3.
if his sister is y years old now, then his sister's age 3 years ago has to be y - 3.
3 years ago, he was one third his sister's age.
this leads to:
(x-3) = 1/3 * (y-3)
In a year's time, Evan's age doubled will match his sister's age.
in one year, evan's age will be x + 1.
in one year evan's sister's age will be y + 1.
this leads to:
2 * (x+1) = (y + 1)
you have two equations that need to be solved simultaneously.
they are:
x-3 = 1/3 * (y-3)
2 * (x+1) = y+1
you can solve these two equations by any of the methods that you learend for solving two equations simultaneously.
i'll use substitution, but you can also use elimination or by graphing.
in your first equations, solve for x to get:
x = 1/3 * (y-3) + 3
simplify this to get:
x = 1/3 * y - 1/3 * 3 + 3
simplify further to get:
x = 1/3 * y - 1 + 3
simplify further to get:
x = 1/3 * y + 2
replace x with 1/3 * y + 2 in the second equation to get:
2 * (x+1) = y+1 becomes:
2 * (1/3 * y + 2 + 1) = y + 1 which becomes:
2/3 * y + 4 + 2 = y + 1 which becomes:
2/3 * y + 6 = y + 1
subtract 2/3 * y from both sides of this equation and subtract 1 from both sides of this equation to get:
5 = 1/3 * y
multiply both sides of this equation by 3 and solve for y to get:
y = 15
go back to either of your original equations and solve for x.
your original equations are:
x-3 = 1/3 * (y-3)
2 * (x+1) = y+1
in the first equation, replace y with 15 to get:
x-3 = 1/3 * (15-3) which becomes:
x-3 = 1/3 * 12) which becomes:
x-3 = 4 which becomes:
x = 7
you now have x = 7 and y = 15.
go back to the second original equation and replace x with 7 and y with 15 to see if that equation is true.
the second original equation is:
2 * (x+1) = y+1 which becomes:
2 * (7+1) = (15+1) which becomes:
2 * 8 = 16 which becomes:
16 = 16 which is true.
looks like the value of x = 7 and y = 15 is a solution to this problem.
x is evan's age.
y is his sister's age.
go back to the original problem statements to see if these values make those statements true.
the original statements are:
Three years ago, Evan was one third of his sister's age. In a year's time, Evan's age doubled will match his sister's age. How old is Evan now?
evan is 7 now and his sister is 15 now.
3 years ago he was 4 and she was 12.
4 is equal to 1/3 * 12 so the first statement is true.
in a year's time, evan's age doubled will match his sister's age.
in a years' time he will be 8 and you multiply that by 2 to get 16.
in a years' time she will be 15 + 1 = 16.
values look good.
answer to the question is:
evan is 7 years old now.
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