SOLUTION: Pls help. Elias and Shui are good friends. This year Elias is 48 years older than Shui. Nine years ago Elias was three times Shui's age. How old is Elias?

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Question 1196562: Pls help.
Elias and Shui are good friends. This year Elias is 48 years older than Shui. Nine years
ago Elias was three times Shui's age. How old is Elias?
Found 3 solutions by amoresroy, Theo, greenestamps:
Answer by amoresroy(361) About Me  (Show Source):
You can put this solution on YOUR website!
let x = age of Shui
x+48 = age of Elias
x-9 = age of Shui 9 years ago
x+48-9 = age of Elias 9 years ago
Equation
x+48-9 = 3(x-9)
x + 39 = 3x - 27
39+27 = 3x - x
2x = 66
x = 66/2 = 33
So Elias is 33 + 48 = 81
Answer
Elias is 81 years old.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x = the current age of elias.
let y = the current age of shui.
x = y + 48 means elias is currently 48 years older than shui.
x - 9 = 3 * (y - 9) means that elias was 3 times as old as shui 9 years ago.
replace x in the second equation with y + 48 from the first equation to get:
y + 48 - 9 = 3 * (y - 9)
simplify to get:
y + 39 = 3y - 27
subtract y from both sides of the equation and add 27 to both sides of the eqution to get:
39 + 27 = 3y - y
combine like terms to get:
66 = 2y
solve for y to get:
y = 33
since x = y + 48, then x = 48 + 33 = 81.
you have x = 81 and y = 33
9 years ago, x would have been 81 - 9 = 72 and y would have been 33 - 9 = 24.
72 is equal to 3 * 24, confirming the requirements of the problem.
your solution is that elias is 81 years old.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The two responses you have received to now both show the same method of solution; that method sets up the problem starting with the statement that Elias is 48 years older than Shui.

I would start the problem differently, resulting in easier algebra....

Since Elias was 3 times as old as Shui 9 years ago, let x and 3x be their ages 9 years ago.
The difference between their ages 9 years ago is then 3x-x=2x.
But the difference in their ages is 48 years; so 2x=48 and x=24.
So their ages 9 years ago were x=24 and 3x=72.
So now the age of Elias is 72+9=81.

ANSWER: 81

Without all the words....

x = age of Shiu 9 years ago
3x = age of Elias 9 years ago
3x-x = 2x = 48; x = 48/2 = 24; 3x = 3(24) = 72
Elias's age now: 72+9 = 81