SOLUTION: martha is x years old her brother is 2.5 times older than her her father is 4 times the brothers age the sum of their ages is 54 work out their ages

Question 1176931: martha is x years old
her brother is 2.5 times older than her
her father is 4 times the brothers age
the sum of their ages is 54
work out their ages
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
she is x, brother 2.5x, and father 10x
13.5x-54
x=4
she is 4
brother is 10
father is 40
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Defective statement of problem. No reasonable solution.

Martha's age is x.

Her brother is 2.5 TIMES OLDER THAN HER. That is NOT the same as 2.5 TIMES AS OLD AS HER. 2.5 times as old would make her brother's age 2.5x -- as wrongly interpreted in the response from the other tutor. But 2.5 times OLDER THAN would make her brother's age x plus 2.5x, or 3.5x.

So if the wording of the problem is interpreted in the grammatically correct way, her brother's age is 3.5x.

Then her father's age is 4 times her brother's age, which is 14x.

Then

That is not a whole number, so the problem is defective.

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BEWARE any problem in which the phrase "3 times greater than" or "4 times older than" or anything similar is used. The probability is very high that the intended information was "3 times as great as" or "4 times as old as".

Regardless, it is impossible to know for sure which interpretation was intended.

In everyday usage, the two phrases are used to mean the same thing; but grammatically they are different, and they mean different things. The phrases with "...older than" or "...greater than" should NEVER be used in the statement of a math problem.

I have seen incorrectly worded problems like this many times on test questions in math competitions; I even once saw one on an SAT practice test.

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