Question 1123405: Suppose your sister was 1 more than 2 times older than you. Suppose than in 4 years your sister will be 6 more than 1.5 times older than you. Using this information, find your current age.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! "You", 22
Sister, 67
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your sister was 1 more than 2 times older than you.
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x=3y+1
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in 4 years your sister will be 6 more than 1.5 times older than you.
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x+4=6+2.5(y+4)
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
I will show a solution for the problem exactly as you show it... which will almost certainly not be the answer that the author of the problem thinks is right.
The problem is with phrases like "... 2 times older than...", which are almost always used incorrectly.
The problem as you show it says "your sister is 1 more than 2 times older than you". If "x" is your age, the intended interpretation of your sister's age is almost certainly "2x+1".
But that is grammatically incorrect. "2 times older than x" means x, plus 2 times x, which makes 3x. That is, "2 times OLDER THAN" means "3 times AS OLD AS". So the grammatically correct interpretation of the given information is that, if your age is x, your sister's age is 3x+1... NOT 2x+1.
And in the other part of the problem, "1.5 times older than..." means "2.5 times as old as...".
So I will work the problem the way it is stated. If you want to get the answer the author of the problem probably intended, you can change the numbers and work it that way.
Let x be your current age; then your sister's current age is 3x+1.
In 4 years, your age will be x+4 and your sister's age will be 3x+1+4 = 3x+5.
The problem says your sister's age in 4 years will be 6 more than 2.5 times AS OLD AS you then:
3x+5 = 2.5(x+4)+6
3x+5 = 2.5x+10+6 = 2.5x+16
0.5x = 11
x = 22
Your age is x=22; your sister's age is 3(22)+1 = 67.
Yeah, right.... 45 years difference in the age of siblings....?!
But that's the solution to the problem as it is written.........
CHECK:
your age now: 22
your sister's age now: 67
your age in 4 years: 26
your sister's age in 4 years: 71
2.5(26)+6 = 65+6 = 71 check!
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