SOLUTION: James dad is 5 times older than james and james is twice as old as his sister sara. In two years, the sum of their ages will be 58. How old is james now.

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Question 965112: James dad is 5 times older than james and james is twice as old as his sister sara. In two years, the sum of their ages will be 58. How old is james now.
Found 3 solutions by CubeyThePenguin, greenestamps, josgarithmetic:
Answer by CubeyThePenguin(3113)   (Show Source): You can put this solution on YOUR website!
x = dad's age
y = James's age
z = Sara's age

x = 5y = 10z
y = 2z

(x + 2) + (y + 2) + (z + 2) = 58
x + y + z = 52
10z + 2z + z = 52
13z = 52
z = 4

James's age = y = 2z = 8
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


There is no solution in whole numbers; the statement of the problem is faulty.

"...5 times older than..." is

NOT

the same as "...5 times as old as...".

If James's age is x and his father is 5 times AS OLD AS James, then his father's age is clearly 5 times x, or 5x.

But if James's age is x and his father is 5 times OLDER THAN James, then his father's age is x, PLUS 5 TIMES MORE x, or x+5x = 6x.

So in this problem, if x is James's age, then his dad's age is 6x and his sister's age is (1/2)x. That, with the given information about the sum of their ages 2 years from now, leads to a non-integer value for x, making the problem faulty and unsolvable.

Unfortunately, in everyday language, "5 times older than" and "5 times as old as" are carelessly used to mean the same thing; but grammatically that is incorrect; they mean different things.

Bottom line:
*****************************************************************************
*  Phrases like "3 times older than" or "4 times greater than" should NEVER *
*   be used in the statement of a math problem.                             *
*****************************************************************************
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
James              2x
Dad                2x+5*2x=12x
Sara, sister        x
SUM, in two years   58


.
.
, just for Sara's age.
Fifteenths is not the best denomination for time based on some years. Wanted are denominations of months, or weeks, or days, or whole years.

Recheck the problem description.
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